Question
The angles of a triangle are in the ratio 3:5:10. Then ratio of smallest to greatest side is
Hint:
The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.
The correct answer is: ![1 colon 2 cos space 10 to the power of ring operator](data:image/png;base64,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)
![T h e space a n g l e s space o f space t h e space t r i a n g l e space A B C space a r e space d e n o t e d space b y space A comma space B comma space C space a n d space t h e space c o r r e s p o n d i n g space o p p o s i t e space s i d e s space b y space a comma space b comma space c.
s o space W e space k n o w space t h a t comma space
fraction numerator a over denominator sin space A end fraction space equals space fraction numerator b over denominator sin space B end fraction space equals space fraction numerator c over denominator sin space C end fraction space equals 2 R](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAx4AAABUCAYAAAAMEeGpAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAqG59bSAAAFR5JREFUeNrtnX2kV9n6wJfjSJJIkmREMpL5I0aSkUSuJEmMZCRH5BrXyIiMJBlDMkaSHxlJkjhyXCP5kRxJxnAlGUnkGiMjcSQ5kjh3Pe3nW/usWXvvZ799Xz8fHud8135Zz3rWs9fLXi/bOeh3xryswAwAAAAAMCyN27de5nLkrZ4nzKb+Hyb6LV07vMyo/O5lfAjS1G96taXHkYLjb7y88/KHl6defvGyMnLeGi9nvDxQXeX8770s5dkamHR1M+1HGrqP1T+t9LMf18mfYfXrYSaWZ+Tj4Pq/VYdu6ToovtR3en6qFUSMtV4eDuED1G/pkk7GMy8b9Pf6At3v9SBNWfEOiq3b0mOfdtTHc+INny9phF0Kwo56ueFlS6qA+EQbl5d4trriq3XT1c20F/ldmXRZ/NNKP/uxNQ/v9alfQ/38Jh+bsWUbZWxTdUu38nhQfKkv9dzr5WrGsT1erg3hQ9Rv6dpbQp+s/Go7TXl+Mqp5vlQf6Ft6/6x4rxbY8piXn3m2+tpXLenqVtotflcmXVcbsl+/+7Elf3pVvsLw1/PDRD+3B7qV74PiX32p5ymXvKWKcVIrk2VefvLy3CVTgb6JnCtrE667ZNhehta3GuIe0/jlvvL2Tt68rY7ocFTvL2/MZnN0WOSSIf4Xqofoc17TEEtXWf2P6zGZljAXuUeM5V4uenmt977sZaFBn6z8SE+JO9alvLLE+08v/9F7HstJ26DleR4XvOz3clDjzHuG0ogP7ND/ZcRRprdUfXNttWdeHlW1w2Iv57y8LLB90f3L5HfR85Tnq9a0WtMVy+vjmh9/6bXTbv60JdF9X+RaGRH4oUG/s1Lkn1a65cdWP6mSh70qX9M6S1n2TG0w5eZPTytTl8Se9SbKgbw60OL/ZdPSdH6fjOjcdF1Tpx1gsV/Tdra0bU4GflS3jHU1dWi6DqrSvmuzvLeUh2XKeKu/uIbKqkIkM3ZnHJtUpe/qOWKMVar4otR5S/QNXOc+MlXod0PcN9Rpluq9JyNv8Ca1ELikzpKlg1R4d9RZxlW+VSeK3XNPSf2P69u8BRXeTE6o3ku053kmdc5U8BDvL7jnZMZbzrbzKi9ecb4fXTK3u+i6QcrzPDZrWjqF2tMCu0kaNmhBlJ6b/6OrN1ffas+sPKpqhzEtvNK+3amQytrZmt+W5ynPVy26WNOVlddP1R87+fFT8LbpYERfSeMTbdQ25XdWivzTSrf82OIndfOwF+WrVOT3tTGyROsZaRDvquD7Wc963XKgqA60+H/ZtDSd32H+tlHXuBrptdivaTtb2jYxu1UtY7M6HWV1aLIOqtK+a7O8t5SHTepZttORV1aZeJrT83miBlgchM8ERhPDfhcxXF4m7leDhG/adkZ0OBy5PtThREYP8kkkfU+0cCmjv8xn3F4yg85o4ZRmjcaf5rFL5kFbeJzR820zr4ri3ZtzXdrWg5bnWYzrG8N0nsmDuC5Dl06n8nXkTfIjl8zBrEIZe+7N8dEqdjiR8Uaoip2t+V3meVpdMa3WdGX5+vpIRfwq9XtnJM9OarxN+p2VIv+00i0/tpYLVfOwV+XraW1o1K1L8p71uuVAUR1o8f+yaWk6v8OwNuqaOnlnsV/Tdra0bUK71SljY1TRock6qEr7rq3y3loeNqlnGYrKKlNF9jrnjebroNffuWY2OE+GuZYHYa9c/ir6aX17l+ZO4MxjGfqFOgh/RXqQsevHKur/pVbyu422lWtlSDYc1lyo8WXpU3TP2R7kVV68syWuG7Q8z6IzPJ9GKqWvc3RZoAXbry6ZltI5/qbG82u152xO/lS1w5+RRlgVO1vzu+7zZE2rJV1lnpGFQQG/LHjbtlxf/ixs0O9cifIkzz/L3KcbfmwtF5rOw26Ury9c9lSFJuqSJsqBvDrQ6v9l0tJ0fsfKp6brmqbzLma/Ju1sadvE7FanjI1RVocm66Cq7bu2yntLeega1rPM/fLKKhObNZExNnm5bbhmk4tvyVu040G4vVfsId6UoV+ow+cuGQJ3hus31dB/pcYzHXH4EKtOm3LyIHbtnR7kVV680wXXTQ94noes0wIqRIbpfzHky1fu49DrghpvHeras44dNhj9wXL/pvM7z1eLdNlQ0c+L0nE7km8dZMj7SMN+50qUJ3n+aaWXfhz6Sd087EX5ujHDt5usS5oqB7LqQKv/101LnfyuGkeZuqbpvAvt17SdLW2bJsvYPMro0GQdVKV912Z5bykPy5TxVj0tFJVVJmRI51LJY2G49BAnK8T9Ivj9RaRiteogw8dXjGmoq7/0FGW+4IGC87LuGy4qysuDWHou9yCvysabdXxQ8zzNXZf//ZvxIN6LwfXiN+mdf2JvUrvxDNWxg9X2lvvX9d3Y83S5YlrL+JT1HJnqcCLiQ2tUnjrbKFsZvyvzXBf5p5Ve+XGdcqFfyleZQjHVcl3SZDkQqwOt/l83LU3WA93wqbrpDe3XtJ0tbZuY3S434Ed1dGiyDqrSvmuzvLeUh3Xb+DE9myirTMg8rUM5xyYM10jP6bcKcT9z84ebxAjXjfqF4eJcsYUyVyLXy7WHa+p/Ud8M5iFzpW8GYeJwj9z8OdmhPnmc9fKvHuRVXryHSvjXIOe503uczTl+zc2fhxnLl4tu/gYC8vtoxee3jj3r2GFPRmF+pYKdrfltfZ6yfNWiizVd1vJygVZi4Rzwy+q/Vw0VXBW/K1P+F/lnmTKxF34chtfJw16Vr/J2+nFDdcmhCnV9E3Wg1f/rpqVOfofXtlHX1Mk7i/2atrOlbRPao04ZW7V9VTXf22rftVneW8rDOmV8lp5NlFUmpnIqrKxjsfBH2pMWx5a5X7KQZ0tB3PKRqgt6zWrNlJsVdZCFMrLtWOcDfBs0oyQDtzas/0Y9v2gHms5HATsr/Vdp3MdL5EHI+cgbym7kVdl4s44Pap47fUjlYc0bgj0UNBCn3MfFujK3U+aRPnDzF7WJHWY0/qWpty671ObbW3qG6vjDIr1uQ6owuqG2L2tna35bn6csX7XoUiZdMX2fpPKro99ExlvHi872UacqfieNJMsOThb/tN6rV34chtfJw16Vr07t/oP6+RK9xxcN1iVNlgOxOtDq/3XTUie/w2vbqGvqtAMs9mvazpa2TWiPOmVsEVYdmqyDqrTv2irvreWhtWwuo6e1rM8rqzp0RuOjzLjsRS5Zx2LhMoQkw0nvNNMOGQ18XHutJ/Sez4NEl9FBepSyB7NMO5CdX/7hkiGrsQb0f6lGlOPTzr6LzBa931vtJU6UzIOQ9fpgzQWNg7bzqmy8eccHJc9DJl3xdnGr3PwdQ2ZSD+AbfbBju+qs1bcir/Tcl1qx7WzxGar77K7QAkzSJQuSt1W0c5n8tjxPWb5qTas1XSHP1R+f6P0fuPyPSs4520LGKn5nrUAs/mm9V6/8OBZeNQ97Vb4KslPZHb3uYeS6unVJ3XKgqA6c0fyy+H+dtNTJ7zCsjbqmTnot9mvazpa2TWiPumVsEzo0WQdVad+1Vd5by0Nr2VxGT2tZX1RWFXY8+o3lDd7rM9f/X5WU9P7lRptRy/NBsie0w26tKNuk6vSrtu+FHw8fC7TBN0o0WddY7TeKdqa8zy8Pmy6be1HWDyzSQ/0/93HOmgyX3XP19rdvm7P6FuI02TcyeQ4gyLD55hbvL9MPZAvH8T67FwwnjSw4HeG6xmq/Ybcz5X1vy2bK+pLI/GdZRCM7q8xqRn/W5zrLnMS9ZN1I5TmA+OiNluOQ6VIr+vBeMJwcdDU/KDbidY3VfsNuZ8r73pbNlPUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAkM8TL8uCsDEX/3rjOj2/LrMax7AwbOkBAAAAAGicX7xsC8IOeHkVOfe8l29rxrfWy8MBtJPofa/l9GTFAQAAAAAw8Ex62RWE3deOR/ot/mIvL/RvHfZ4uTaAdtrr5WrL6cmKAwAAAACgaxz38oeXd17mvBwLji/3ctHLay9vvFz2stBwX7nmy9TvLV5uebnp5bNU+BEvPwXXrvByXeMT3bYa4juZ0n1c9dwZOeeo3v+SS6YyzXj5JnK/vHRnNeS/1/uH3A7SnNZnLiXHIulZpvZ5nqGrdOJO6fG3Xh54WW2MAwAAAACga52On70syDi+1CXTfSa0gbvEJW/hzxjufcLLwdRvWduxTa9Pj4Q8dslUoA5LNM7d+nu9l98N8ckIyx7tHEy6v0/z6pzzjXY6tmqaVmnHYlGJdK+N6CT3eaJxpNmsnagivWPh0mm4q7bI0lXsek51Hsu4X1YcAAAAAABdQeb9b885Lg3tcO3FGmdbCC7rOU7r/5+65E28047OAf1/h5f/j8T5XRB2I6dz1EF0klEFWVuyKeecw5FwGUlYVjLd4cLvi5qePyM2Xpejt3S8VmfoKulenKPr/khHJzbSkxUHAAAAAEBXkKlQsu5id+SYNKpl7UU4rUp+vzTce682xgVZPN4Z/fjGfRw5kE7H1iBOuffyICxcFxLTVToCv7r4lKbOOa8j4eN6bdl0S1wb9X+J806qkb801bGaNOidpeuiAl2nXTKikuZO0MnIigMAAAAAoKusdMl0HmnEpt+uf67hIZv03CKk0S3rIOTt/NNUx2GflysuGQV5FLn3XESKdmTq6LQ/1dmx6r05CLem+7KmRbil1zntaHQ6cjLKs65A7zsZ4bcNuoajLrHOVVYcAAAAAABdR97my5qGA6mw3S7+tl4Wg/9guKesg/i3m7/oW5D1HTIdShZMfx1ckxVnEdLhuKT//+jlnwXn5IVb0y26y0jONk1nh1OaZsuuVPu1A1NV1xfB8S9cMoJliQMAAAA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The angles of a triangle are in the ratio 3:5:10.
![sin A space colon space sin B space colon space sin C space equals space 3 space colon space 5 space colon space 10
space fraction numerator a over denominator 2 R end fraction space colon space fraction numerator b over denominator 2 R end fraction space colon space fraction numerator c over denominator 2 R end fraction space equals space 3 space colon space 5 space colon space 10 space space space space space space space space space space space space space space space space space space space space left curly bracket space space S o space L e t s space 3 x space plus space 5 x space plus space 10 space x space equals space 180 degree space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 18 x space equals 180 degree space space rightwards double arrow x space equals space 10 degree space space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space S o comma space space A equals space 30 degree space space B space equals space 50 degree comma space space C space equals space 100 degree space space right curly bracket
space left curly bracket space fraction numerator a over denominator 2 R end fraction equals 3 semicolon space fraction numerator b over denominator 2 R end fraction equals 5 semicolon space fraction numerator c over denominator 2 R end fraction equals 10 space right curly bracket
space space a equals 6 R semicolon space b equals 10 R semicolon space c equals 20 R 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)
If a triangle has sides a, b, and c, then ratio of smallest to greatest side is
According to question,
Then ratio of smallest to greatest side is
![fraction numerator a space over denominator c end fraction equals fraction numerator sin space 30 degree over denominator sin space 100 degree end fraction space equals space fraction numerator 1 over denominator 2 space cross times space cos space 10 degree end fraction space space
left curly bracket space b c z space o f space a n g l e space C space i s space g r e a t e s t comma space c space s i d e space i s space g r e a t e r space t h a n space o t h r e s space divided by divided by space a n g l e space A space i s space s m a l l e s t comma space a space s i d e space i s space s m a l l e r space t h a n space o t h r e s space right curly bracket
fraction numerator 6 R over denominator 20 R end fraction space equals space fraction numerator 3 R over denominator 10 R end fraction space equals 3 over 10 space equals space fraction numerator 1 over denominator 2 space cross times space cos space 10 degree end 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If a triangle has sides a, b, and c, then ratio of smallest to greatest side is
According to question,
Then ratio of smallest to greatest side is
A triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.
Related Questions to study
Consider a body as shown in figure, consisting of two identical bulls, each of mass M connected by a light rigid rod. If an impulse J=MV is imparted to the body at one of its ends, what would be its angular velocity. What is V ?
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Aj1NY2wxk1GQuOPRZTx5WptPxc0FRpbGKKiofy8/T1bOYBNcbGD/C+8dZbWHbXLxWpxbn6g8CQ2JgxY9Qn9y699FKMEpXWHDOwxDa0wJbriW56g2nt7lvd5OCVTKG9fvtzDTHO/sTLflDJeOihh/D4449j27ZtahUWDtybRV25dPhVV16Nw+cdodZwM0NlfiGtpobduPm6n+DBB36LzY0tiCKCGTOPwE//43ocs3AWcgMtyKtrxD3X/idu+s0D2CbxGpIjMOOkc/Cz/7gMSw6fAr9wgi8ZVaQW8/GTjWK9ieilEjSymdhEu3Tw1urVuO3WW/GnP/1JVeKuXbuEwWvVMsV08yPJv/71r3H//fejvr7ejWphkQnmwu9u2x16O37ggN8VYX+7VfrkW6JwbN26VfVH9j0uza8sK9HI/vMn/4n31qyVqnNnKt0/ukLBAILqkQ4/KqdM0cv6b96qwoYCfvWl+S119Rg1phwHT6mkeiaE6UdQRN0uJF7HTSN7+KrP8O+o24MV/+9RPCakxm+HGtalRubVylihDz74IN59991OGp13azE0MNDW6ohPh1cUMnl2HExDetjuwh04YN969tln1Td9qVRwn+YmTU9+V8SMb1N749fEqNG1tLUqP/VYh5iifp+DSDisJhFCoTAWLDwGZSVl+PijD7FX+jhDbdyyHVvrmjB56lRMr6xQmh7jMl22gqbKzi2TEv7SIVvXmW3wvfzWm87Prr8ej694BGpNdSG2dDOTlckK5tffL7nkEvX5PX5f1ITLJhXUondIMw/oelStLQnI1aL2O6dGNw+6WwVue7tG3OMsXJ/BsP0Jn52gack+xiXaqZXdfffd+N3vfqf2DZGxj1HYDwkSHZ8zO+aYY/HLXy3DpOmTpO64UGUb2hrqsOzGW3HXncuwPRnApZf/EGvfWItkazv+/crv4ch5M3D3fz+Ixx5+CqeeOAd7dq3D9Q89jarFf4sf//AynDRvCkLxBAIOTVG/a4r6xBTlYyAG9NFXgOn/pumygQ98T7/0snPTjT/DX55+Bk6ssybGwgdFpWXlclaGBS4vL1djbrx7mBPIhhOx6DsU5QygycwiE5mTMPd62fYnD5UmI/QnUn/DZyfYf0hY7GPc7ty5U5me9PdaRV6FQysbCRw0fQZuvvV2LFx0nPRJH0JoRdve3fjlDTdj2d33YWcoH5ddcz121WzHX1c+h3+8dCmOO/ZI/OKmh7BmdQ3+8dtfxeb3nsUP73sCB51xEa77wWU4ce4UhJ0Egi6xxYXYiBSxya9cQPqFBE24RHYR28t/VcT2zFNPCbHpgpv6Y/mCcjeh7U0V1Xz0g+BdxpxANpyIRd/B5rXEll3g5ADBvuT9lGUmYuOW4bg7ZfI0/PzGm3DC17+OcNgvxNaCtvrduPPnN2H58ofQkFeCq396M5x9bbj3jjuw5PQFOOroQ3DnsqeQSJbhsv91DNb85W5cdd+fMfnUi3Dtlf/mEpuYtEJsfNwj4eO0AYkt9ZqVl9g6QB7gfxbwge/pV1Y5vyCxPfmkGPgpVdPvd6dZ5AT5BDLvJPwq1Yknnijq7zHq2TZTwYQlt6EDl5cGjM4tblL1bkV6uiw6FcQE7M91xLD9CZ+dMM+IUnFobGzE008/rR7tIAyZaSLT5EZtjdLeHsXcOfNw5y/vxqw5c4Rokgj7hNj27tHEdv9vERs5Fj+55Q6MjuThp9f8EBWTijFzzsF4+In3MPPQE/DDvz0GLzxwLf7tV49i/NcuxDVXXo4TDiexST6K2CDEprmAX2PQtS2/2U5sqzd97Pzs+h/jd8uXSwULJ5PcpGDhSERU4yQSsaj4+9QdhV+A/8lPfoLTTjtNfcy1P8SWDSdrodGJTwaAzi3qElkHjLun3DJdE/25Thh26F9X7BskKlpFnL286667cPvttyuT1IDkRzAcQUUjLzcP3zz7HNxw440oKi1V/TXiEtvtN94sGttv4CufiJ/ecivmThmNa6/4Pt79oAa5JeOxaXczzr/4n/Cj84/HYzdfgctv/gPGH/MdXPXv/4aFR04TM1SIDUJskldC8qSW3kFs4lbja1Ju1QKa4ZR2p45kQ1/fF0s6dy6/1xk7caITiuQ44Zxcxx8MOcFwxAkEw47PH3CkMp3CwkJn6dKlztq1ax2pVCeRSHQSaZRuxeJAAJ+IzCSxHiRT+P7I8Lu22F+qq6ud73znO+QUJex/QhbKLWaqI9aSch988EznT396zBGlw2mV6miOJpx4rNFpqv3E+dkV/+JUlZc6h8w50nnixRed5oaNzg/++XRn8rjRTtmYmc6Ig+c5V//+YSeWrHPuv/oCZ3wk6Jx08kXOypc3OU1RppV02qLtIm1Oc7zdaYm1O+0iMdmnxOVYQvZF8ZGmkLZMxqXsmgeyAf78oA+nLzkF3/3u32PihEpE29tEa4tBCo5EXBg7mVBvHZxwwgm4+OKLMW3aNHXXkLgdajJh9q1Y6SKZ/jKFs6L60vTp0yFKBI466ii1L2ShjlETouXU2tqqrKelS8/FwoUL1Qwpo/KtAPXFeFdz0mnypXi/aHwRVFRUSl8Ooa11H0aXFqOseAT4cEebE0Rr3H3Ugyt4SFp6aQzRDiUtJpcSV1PjYRfMm/GyCYErrrnmRwX5I6QyJ6O8pASRUFBVUEtzI0pGFuOII+bh1CWn4lt/8zc4+uijO42t6QrsHX0NZzGU0d2FLf7dNv9ArwvGH37XFvvX2LFjlRJRUFCg/EhoNEcrKyuxaNEinHfeeTjnnHNVOPYvPs+gzcU44u0teGPVa3hn9RqECkbipMWnoHJsMZoa6vD26g34ZOsOfOW4o7H41JMxsaQQm955Gy+/uR4lFQdhwVcXCgGWqfGzABc1ky1NTHZhfmqWtU1JwZCce0SF7Rziy4CvSdRXH1oRkUprbWhETc0n2LBhg3ogN18I76AZMzBl6lSMGl2OUCSsrlM/n0pm4TtOiLvdn4wltuEGQ2Jm2xN6CqPHizKD8Sg9XTs8NvyuLaM4cByNbwLxfW2+bWA0tVmzZmHSpElqMk+NzUkdRDkJLfFy0IbWvbW45ec34p7lv0HxpBm44bbbMP+wCVjz+gv40TU3YeULr+P8f7kUl175fzG7rBiP3nU7rrz2DlRUHYcf/fgazJ8/Q7S3BHIiHPujTieJS9p8J4HkqWfFXUIT9lAvKcjWUWNtWUJsbWJL+3zNCIgqGUi6F4pbQFViVcY0P1Fv5Tz7PFhoiW24QV3Znu3+wL2eukVf8ugtjaENQ3AGNBUJEh79zYRCQignJtUUkPCRZBvirY14/ZVX8Obq9xAqG4eTTj8T08eVYvvWajz9+LPYUrMNhy5agCOO/yrGiQW24Y038OSzq5FfWoWvL1mE8ZWFaI86Yray2zNPEhvpU8oiPMEH+Vnvumip/p9Nkwe+eFyIDc1c+wTqM/rKVwqmhMTmFlLRsutHYhO3vuQssR146Avp9AZeEz1dF33Jo7c0hg/48C4fB+FL8GbMzcyQktjiUk0ktrAQG5Ixt2pCiAZy0C7ufAmaTOyDPyqhfWHEhLTaxC8i6YbZ7wNi8ko41nacKySJlztfIc6Eyk+BW2ppbr2zbyu3iku/3vngi4Cfj3LQtNQztvpEuko6WHj3pCxpWVgMKkgiHUQiIKm9+eab6h1So615+x1dpDjlY/z54qgQX1j6d450bqoi8AflXxiNa63FY6LIaMuLRJUUL3qLVwdIWPxTKTNdEWplNDmV0C1HqcClSpsdEANdiiQlE0NUCm6E1WSqyitepO9bWHSH9OvISE/o7fjwhJfUzJbPs/Gl+Icffli9GM/1EY1ZquGlFapa0of5gL1Lcnq5Idn6ckUzCylCCso2VzS3SDAHCIm43Z1KoFkFiXG6toL2UTmK05BaJvkywdORQrAyRPgYhxqM9IioqcrsVCXlSUnFK6amW5+khUX3MNdJuvQF/Q0/9GE0MS+5cdmwVatW4cMPP1TbLpaShGFHVp2Z/iS1IF/LEh/ynyRFzSupdsQViUh3D8lRxiDtiSvAZYtSlEQLjkeZixb3lzyhRPZdUeSmDrv74kyl9OWAD71IYQJSCApJLOWWA7qwHVvCbC0sLD4PcOzMEBdfhufquVyi6L333lPLFFGD66SxKRYRhYNuRqPa1dFfBXJAz2aqgyLUxyhuH1f+KhERL/RIekqJ0aRlkB46m8AZXCmgnKCwPL9G47iamxY5edmnnzpFd6tP0sLC4vMASctoZRxbe/7559XEAb99QO2Ny4Vz3M2EId24PdR1GSHcHivkxQd12eWVqUpicyj0IwmYPs1YJE1X1RMwB/5yryfJJvCsXOjCmzuFhYXFlwOSFsFvHrzwwguK3Eh2fDiez5dy+X4uCkuoMTmXWjrrU+kwx3Q/T0nvMKHSY/Ul9pdFeH5WTAfzu0KkE1z6voWFxecDs2wRx9NefPFFRWrma3GcOOBy4TRNjdaWiHM6U1OIIjrlZH8VrU3te8zW/YROja9saeGXRs2f8UsHi2Hki4ZHY0vBkpqFxZcHmp179uxR2to777yj/EhiNEX59sHHH3+sljZqbm7WxKVCGLCvGjlw0S2xecXCwuKLA98ooFb2yiuvKE2ttLS0Yyn+wsJC9e1fHuOkAglPf7lKdCbpqlrYbzv34wMNGYnNwqJnmI7CbV9kIDDx09M0MvxAjW3lypVqFpQvvH/7299W74eaF+C50Cu1N35VjppdSmvz1kl/60bCcwLBSEda3Yv56+zfeS/l+8XC72X17tg9U5j+iMVwxBfZrgfONUSS2rhxo/oo8pIlS3D11Verb/ryQ0rU5I4//njccsstOP/889WL8S+//LLS4HzmEQ9XvByleUp+1MNprii/NPHiyxgYG0RYjc1iAMjUO9JlsPB5pp1d4Pd8TznlFFx33XWYO3euWq3avBdKs3PGjBn47ne/iwsvvBA7duxQY20KPVVNn6rLm8D+SAqZfb842DE2C4ssAvvbnDlzcPrpp6Oqqkot8mpIzYCaG9dhO+OMM7B48WI1i0pNL73feuVAg9XYLCyyDJws4AKTXFzSPKxrQLd564BhuNou12UbdPJKS87sctsX+bJhic3CIsugJgNEqKlRO/OSFv14zIDH0jW6/UYvzJQNhNVXWGKzsMhSeEnLkJmX5AwBfpHwcl93kg2wxGZhkUXIRFQkNxIahc+1GbIzfl6ys9CwxGZhkeXwamaWyPoGS2wWFlkEQ1rpBMYJA5KbJba+wRKbhUWWg4RmZkKNWWrRMyyxWVhkObza2qDNgA550DTvfuLE1pKFRZbDO8Zm4YUlNguLIQMzjuY1OUlsXMmDL8hbkiM8ddDhpEPvWGKzsMhyGI2NJinfRhgITFrDA+nnkdq3xGZhMQQwGGT05RAa8zTSE8w3FnQ47unpkpRf1xRSx9Jhic3CIsthCGkgs6EmDW67k8GHIR6vuOi0S4dLZe4y5h3ExnK5M8KdoqTtpcMSm4XFAQIveX0+RJYJPZBxpkNqATlNaqqE/BE/teF+B4xPeiI6lCU2C4thDq9WZsT4e5EpzMBA0jGShgxeGprEUhqbBHTJjv66VJ4QLKf2FHQ4LLFZWByIGFwCM/AQjodkNIuRarxs5g1H4gqK8HunOgzpTVMc973xTMr89ebRGZbYLCwOACgSM1sPoaXv9x+GYEhS/B4qxUNs5rARhYQ442qrPOlveM6FX44F1HENfsmetCcF5U8qqW5gic3CYhiCRJUUMR9f5rpuRvh9BDMR4aM21IUlqC31FQzJBDRZOYhJ3lHZd1mKh41oTpL/qEiT7LRrDx5zP05PN4sWknQCTEP8EsKBiYSrwak0dGJJEh8Dd7CYR+OTCmBQCwuLLAU/tXfttdfik08+wRVXXKG+ddDTq1Wq75PYkkm0NbeiYV8Dtmzdoj62PH16FcZWVGiecZJCAOKiiEqkuU7FFqGfJ4+OYwbKwwWfrYsLzZCw4mhvjmLrJzuwc08L2qJBIakQpk2chMqJpUj6k3D8jSIN2NfQgq2b96ChTvSzthEoKi5E1azxiITj+OTjN7FzV51Yp5UYN34axlXkIifsQzIeUN+iSfrasK9pDz7aVIuG+naUjynEhIljUVBQJGXhB5wtLCyGFUg/CSE1vzBALB7Fa6tW4fLLLsP3Lr4Yz6xciea2ViSE1KjzKKOOdp6K5ZqQar876GMmBuPrP51ee6wNjQ17cd89d+P8887D+X93IS78u0vxwL1/QsPeJKJxvvcqRJhsweuvv4zLr7gc5y49D2ctvUjcN+Ojj3dhb8M+PPnYClx80f/GP3//Mqxdt8nNTTRCR0SILZGMorr6fVzzw2vwtxdchP++7U5s+nC9+NPEtaaohcUwgaEa4QzR1prbmtHc2qw+BuMkkmhpbhENaS/a29qE7OKIkwCEwByfEA2JzAgZgZoaNUIqZUYU6FABUl4KzDeJIPTXtIJiEbZL3rt270LtrlrU1tZj08Yt2PJpLWJiPVKbjLc2YkP1Wrzz7jtyfA/2NbbItlEIN4DikhIcOmsG4rF2bN+2HevXbURTU6PKx/HFRVuLC0G24d017+L996vR2tSO0pJRGFUyGgF/UJXIEpuFxbCA1rZIMRw/y83Nhy/gIBiMIhxJIOYLwAmLmRbOhT8UUmNtJDXFW6IC+ZSWlsDeulpsWl+Nde+vRbWQRvXadSIb8cH767D2/XeFTFZj/fpPsHdvVAiUOXLky69ojaNsOYE85ESYbj0cIR9fwI+c/Bw0NdZj955a0bkkRyHO9pZG1O3aJfmGkJdXIr4jEAiGVBphYcZJkyZgziEzkGhvwZuvr0J9fb1oYzHERFMTvQ/NEn/dxvWoa23FlDlzMXf+0RhVNgpOUo8pWmKzsBjyIClpaHrSI17hSBD+YBOS/jo0J31oTI6EEylSx6OisVHv4miUnkBw0N7eiCeffAwXXngBzjjjdJx22mkiZ4icjlOXnIqTTz4ZXzvxZDEx/wkvPb8WUY79C4Q+SUdoFc2wXUgnGt0hadUg4RffogJMmjYODY2f4t333kabmKKBQBB127ejZsOHKCwowcRJUyW+UKSYzvEEDVqgVEjqa4sWoTAngPUSb+PGj7CvtR1OgF/timHbZ5/ig/Ub5JzimHLsAlQdNgc5OULmfk4gWGKzsBgmIKVpguNvkhMDJAsfZyjbhMz4AEWOmHFBEYZxyZAqmzgdIYhoe7NoRruxZfNm1NSIbK5BzZaPRGqweWsNPttRiz17duOTmh2o29MsGpTOq5PW5giliFblc6IIhIHi0WWYMXMagqF20bDWYs/eBjnux/bNn2H3Z3WYOnk6Ro0qkxQSUi7RyMRMjkm6ubkFGF85ATkhoL52G97/oFrIsVVI0Y9mIeAP1m3Ajl11QE4eRlWOQ2l5iWYz9/UrS2wWFsMWLnlJNw/wEQ93T7GZmKvmKMFhtUhuGCNLijFm7BhMnjwBkydMwqTKyUomVk7B+AnjhGym4KCDZqCgSMzaTuyhyc1RD9rmIJAMC5nRDB2BKdMmoHxsAT77bAt27azF7l37sK56O0L+Qnxl7pGoKC8TwoqJadyKWKIN0VgCofxiiXcQDp09HW3NdXjllVexp74ZAYQUub6y6g1s2b4bk6ZOxeEHT0dprmI1EX1WltgsLIYD+NQWRaAIjNylXQoBITK1z4ExThrIX5J/bhxOFoTDESw+5RTce999+MMfHnblj3hYZMWKFXj8iUfx2OOP4le/+jkWHjNLyEhTCcFUHKEdil9IzZ8IgfMTbUJShcW5mDBhpGh5O/DRpo+EmFqw+dN9yMsrxSFVM1BSnC+k1izmc7PEj+ln7wJ5qJw4FccsPArFI3OxcdMmfPzRFiG9KBrqRWOr/hgtjVEcOe8IHFY1SXRFgU/iKUYjxVpYWAx9CBm0t4jGI6aYWG/wq2fQhGgUcQndyD6f/9KUloI6roMIfMjPy0PF2LGoFDNw0iTR2CaJxibbCRMmYoL4VVSMw6iyEjXhwIU4UtTpghpbMkc4JheJeADhnFyUjS5AxbhcNO7biZoPa7Blax2qN9Ujf8RoVE2oRGEetb0GJHxNCIa5/Dmfyg0ir6AMsw6ZgeKSPGzfvh1vv7UGe3bWY9O6Guysa0PplNmYP/8oVIwqEDqMCcm2SQHs5IGFxfCAS07UdHbX1WPXvn1oj8XQlmxFY3Mj4qI1KVOUD4CJxqYnC8QpbkZNMHo8jkS0FU/9+c+44IILcO6552Dp0m/hW0uXynYpzjnnbJx++pk4Q+R737sSr776vqSrCYTkRmHKtGn9TlhM0YhodDkoHFmCUaOLMGVyCXLCDtZ98AHeWb0Btft8QnbTUJyfh9ywkFGoFb4wZ3B9ahyNpAiJP3HKeMydN0s9k7daiG371s/w3upqbN+xF9NmH4GZM6swIhAXUmsVjS+KuMM3H6zGZmEx9CFk0haNYeXKlfg///J9/Otll+GTmhoE/UEEggH10CpJR2lxQmKKjNRrBprg+BNPJtDU3IzNW7bgrTffxksv/xUvvfSSbCkv4oWXXsBfX34Nr7/2ishr2Fu/lxHTwDE2ISRXfGIg5kRyRTMLYeLkUZg4oRybqtfhiSeeRXM0gmlVs1GQE0JeDhDMdRCMUNMUkhNicjjD4Q9h3OQJWHTCQuRKuDdeW4VHHnlUyrMKze3AjEOPwPiKCsmlTfLiYyBC1mJmJx1OlVhYWAx5JET72lW7Gy8KAT35xBN44/XXsW37Nuz8bA/WrfsIDQ31CIUchII09dzxtg6IqSokGAzlIC+vACUlpRhZVIyRI0diZLGWkuISFBSNQE5ugWhgI1E0coQaY+sMTZY+Hw/4EW0XrbE9jpiQ7oiCPJSPKsW2zZvw9ttviMWah7LyscjN9atXpULhgOTPuO4EALVLR47lFWP27FkYWzEWjU2NePDB3+Dd1WswqnwMZh88CyVFRWoGlsZsh55mNTYLi+GBSDiMsWPHqrG0+p07cdt/3YZL/uGfcImYjQ89+Dhqd36KeXMrMXXyGEQCIYT9Aen8QiQkORG/P4zcSBm+duKp+MVNt+Cee5dh2bK7seyeu3H3smX49a9/jfuX34f7778HP7/xKnxlfhUkSwXSGYkkR35yxIyMRMJCopI+316QI8lEgWhmUzC6dJSQYQPa2z5DXmEY4yaNQTg/oCYEYk0JJJqF0OKisYn2yMdVyG/ACIweXYVDDjlUNL8wtn+2XUzoBL562DQcOakYhZKFL5kj5q+YvghJWYKSpZjDjGphYTGUwbGyBCZNmYzjFx0v2lEBNqxbj2ef+AueW/kGNn24U7SvfCxe/BXMPHgKcsQMpaGodDb1KhX1naCYgbmYOKUKi089A2eedTbO/OaZIqfhG2efIvuyPfNsnHvOuTj56wswbnwB+aMDTCsiP/zYTCIehz/oR1jMx5KRJUKYJQiHxmCKpD1hYokEbhONL1e0rhIkA2I20lyOSnkSASmX4iUopY9KW9yPoqIKHHfsIhQV5IpnUj33tuS4+Th0QikifCfWyZHTiIiERbQaaYnNwmJYwI/Kykpccukl+M5556G0tBQQs7NQSO7Yr34VF/39RViwYCGKCgvVzGmUawEpclP0pkGnen6D2hLNQXF6RX70y+46mBqmc0E/zkfGRONqi3IQX5Qv0cT8TlzMXCAQjKCiYgIqxlZihJShcuxojCwrBvJykV9cKCZpjiQqhCiJKlNZRBfNUe+7HnTQNIwuL1OZVoyvwCGHzlbmMrVCWq0SS4R0zS0nSvR8sIWFRZai12WLpAsn4jEEQiH1StK6jRvw2hur0NrSjOL8QkyonIiJVVPVuFRuMIR2Cct3KvlOJo02ajnkkA6i8pPYlI/eN1DPvymHu+0MUiXfHPDv3YbVrz6HVR83oGL20ThuznSU5zmo3b0T71VXiznZihmz52P+EdOFzGqxccMmvPjKehQWleDEk44TLW+klCqFeCyO2r178Mabb2FzTQ3GlJfjuEWLUF42Cgk5dy7PpMuuaZrkaInNwiLL0ft6bEnVufn8F1+kiiUSnChVD+WSutjFhcrU+Bs7fpxLFonpGlBk4JKbuNQu0eHoHYY8uKUWxzXeQtF9or61oz0kpqaQbYhHo01qssEX4FN2op0RUi7HxwUnWcY8RUgpMEW9z3PjJGlQys884iRPNS4o56vG4hwhNobVxEbx1o6FhcWQhO7khly4Qi534omkkFwcXJuNHnzai6tnkEBIcoY4GG+gMDSkSsHnNsL5ko+UR+xTPkricOUOvqfKF0y5dlG7xKFJLDHEYBXyknKKGZuIk6S58q8ma4oyNaW8NHWJYDAo5q2rZdLDJTX3dBQssVlYDHnojq3JxX3UQTq7p5+7ITIhzTdzoG7B/CjUFf2iBbIMDpdI8olmJqYrFzMSfUzcUirlz8F9TbREUlEhtUaTtZCaaGEMwde99IieOdYVJDwSqA6VgiU2C4shDkUmyuV2fyEEv3gYw4zHOPnJoTPtT5AN2P3p4Y6dudF7B0MbIQWJLiWkxn2mSLJKCIHRwA1x8kD8OaDPo0lqliofLidOAuNbnkJ2fCOCJrJKU0OH07kQ3RdPztQclC3NUktsFhZDHN4Or9z8yeTp9SPS9w1X9QgTSOlU9OgKputqjF7pAHdcFY3kp0LSfHb9FAtTFHQ6PRdMh/DCEpuFxbCCSxTaqTQZ5UOi0Tv6kLuv/FyIoqdpi1sl1J/4R02KQlPTuL3H5C+VjEpTzUwaoZ+kp7hKtESHZql6nIPTFvqP+46Qm7JYecgTnx4qqvrV0PspMBfzR1his7AYbtB9W28UMajdviGdMVIs5wq1NAYw23TQz4iA+bsFoJMGqVqG3C2TNlPT0+lPgTPDEpuFxTCD0luERcz3Q7XW4x7cb7hkpdQuQ2pphOSqZT45TmGeSjsTYRlodmrCESqjv8AvRElJFU9F0jIAWGKzsBgmIBUYOug/LZCUZONNpAPiofy9AYz0gF4OExlT6UPSvcESm4XFMIDhghQfdGYGpcX19Kc0OwnXSYy/CuH507qX16fbP28a+yGSxH7BEpuFxTDDfnLBsIIlNguLYQiSm+g8HX8HGiyxWVgMMxga0+TWN8kMMznAbfehOqNvKaeQHl7TcIeo+QjxM+I9lkEMLLFZWAxDeDt5X9B9eENuRDp9pKO/uXYGaavLnxprk2Ou9AYTxBKbhcUwBTt5X6UrSGheUvMicwyNnlPtDG9YHT7dp79iYJctsrCwGHawGpuFhcWwgyU2CwuLYQbg/wOLwfV26XMpbwAAAABJRU5ErkJggg==)
Consider a body as shown in figure, consisting of two identical bulls, each of mass M connected by a light rigid rod. If an impulse J=MV is imparted to the body at one of its ends, what would be its angular velocity. What is V ?
![](data:image/png;base64,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)
11H2 1H and 3 1H will have the same
11H2 1H and 3 1H will have the same
The sides of a triangle are
and
for some
.Then the greatest angle of the triangle is
The law of cosines generalizes the Pythagorean formula to all triangles. It says that c2, the square of one side of the triangle, is equal to a2 + b2, the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.
![law of cosines](https://www2.clarku.edu/~djoyce/trig/lawofcosines.jpg)
The sides of a triangle are
and
for some
.Then the greatest angle of the triangle is
The law of cosines generalizes the Pythagorean formula to all triangles. It says that c2, the square of one side of the triangle, is equal to a2 + b2, the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.
![law of cosines](https://www2.clarku.edu/~djoyce/trig/lawofcosines.jpg)
A cubical block of side a is moving with velocity V on a horizontal smooth plane as shown in figure. It hits a ridge at point O. The angular speed of the block after it hits 0 is
A cubical block of side a is moving with velocity V on a horizontal smooth plane as shown in figure. It hits a ridge at point O. The angular speed of the block after it hits 0 is
A uniform rod of length 2 L is placed with one end in contact with horizontal and is then inclined at an angle
to the horizontal and allowed to fall without slipping at contact point. When it becomes horizontal, its angular velocity will be.....
A uniform rod of length 2 L is placed with one end in contact with horizontal and is then inclined at an angle
to the horizontal and allowed to fall without slipping at contact point. When it becomes horizontal, its angular velocity will be.....
If the sides of a triangle are in the ratio then greatest angle is
If the sides of a triangle are in the ratio then greatest angle is
A straight rod of length L has one of its ends at the origin and the other end at x=L If the mass per unit length of rod is given by Ax where A is constant where is its center of mass.
A straight rod of length L has one of its ends at the origin and the other end at x=L If the mass per unit length of rod is given by Ax where A is constant where is its center of mass.
In
then ![4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals](data:image/png;base64,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)
s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.
In
then ![4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK4AAAAQCAYAAACPzETrAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAtdJREFUeNrtmjFoFEEUhodDJEUIiKQIImksgkUISBARO6sgYmMhwSIEROQQCYJFCCIiHBYWdiIiFiKIpApBEAlySLAJh4WEQAqLEI40cojIcRDfw39hHebt7O3N3r4Bf/jh2JvZ/W733c57b9eY8nSL3DD61ABbbNyxsvuYVWmavKmY7zMYY+OOlV1iDq5L5MMBQWcUX/wz5KZC7l/kWqTsRZiDapT8bYDAncFJ1K4mTqgW7lPkr5GyF2EOrmfkxQEC9zG5HkHg3rbywaq5r5DfRMpehDmozpM/4nNW4C6Tv5N7GHcv9d178oUC80KJl9oH5Da5S26RJx3jzqV+qwbu+zgOs++Tf5M3yBMRsCcrNf+B9nDeV8nHMpiD6SiWqklP4PKJeI7xLnWE73zzQmmN/BQnjYP4Le5mrt/bUcTNnLsIrIT9iXAX1sbOQbtFfkQew/HuolaSmNM6zOHMtkXd2plUeF3M2E+v4LwQuoYASOsVeU4Y31XCzdohn7a2jWVcbE3sDdwsfOqGPvC0I7mXAvcq/l2X+wxc37wQ/8ANLElpfRJShbwXfxjcNXQUbI0MGLjDYj+w0oKhBe4XVLV5Atcg72oiUEZzpgq+eWW0k/jzz4zUqKOE+yz27ctlNbLP5mx1lZIqFJk0gpz4urX9A4o80+e8EDpwFJtbwlg7KKrk5hTnpWP7EnlFOfscCjGfSivOTB933EQvyPMF2mGueSG0h4uUiC/6O2FsHawauDk/XBCK5Qnl7Nyb3c4xzmauLHB5ieAHFcet7b5muDQvhB6av33oGvLa1+R1YWy/TfwyuVdRnCWF1AlsW4iAndVCR+EICso7jhWg9AcQWYH7A9t7yJmmhLmb5t9n03nnhdAyOgsruPu2He0w6RFkVdxtFFA7OFZLaOFpZGedRBHcwyqxmJNZnTS98DEutIn+v2RTPbNK3TQ6Xw/kPOtGhNyxsvuYC+kPiEEjVD5ArgIAAAEIdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1uPjQ8L21uPjxtaT5zPC9taT48bW8+KDwvbW8+PG1pPnM8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmE8L21pPjxtbz4pPC9tbz48bW8+KDwvbW8+PG1pPnM8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmI8L21pPjxtbz4pPC9tbz48bW8+KDwvbW8+PG1pPnM8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmM8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PC9tYXRoPp5scUAAAAAASUVORK5CYII=)
s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.