Question
In any ![straight triangle A B C fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis over denominator 4 b squared c squared end fraction equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXIAAAAoCAYAAADjRnEsAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAABxBJREFUeNrtnX9knVcYx4+IqqoQVTNRJaKif0ypmomakT+momLM1MxEmJmYqlEzVTElqmpq/8xE7I8pMTETM6oiImZMTU1V2B/7o6pCTUREhLvzdZ+7vHl37vs+55577j333u+HR3PPfe85T5/z4z0/nnOOMd3PJ1bmDJkTW9BOtBPtlI6diILXrPxKM/zHutiEdqKdaKf224l4GPBcm3XYsdKXiD3OW1nzsFNKuqdsp25Ek/cp26kT6h1RcE4KVDsZsfI4MbusScEqs1OKuqdop27EJ+9TtFMn1Dui5LaVmQjxVjyenbRyv4XpafjUHJ67rGenFHVvJVo7daN9fPK+FXZqR72LXZ6Ikl+sXHSEY7g1a+WFlT0rf1g5HalA3bTyhaT33MqulRUrr0as7MelMj2T/9+SlcHM929YeaiwU4q6NwNt/mvtFKJ3JYLezcAn77V26rR6ZyLXO6Jky8oRR/iylXtiZBSuRXmDxyhQiPsvK9cz6d317C1UPAvTIyu3rAzI//8zKxOZZ46IbcrslKLuzUCb/1o7hehdiaB3M/DJe62dOq3emcj1jijZd4RdkUzO8p2VS5EK1IaVs7mwAc8M9UlvTipLGXsldkpZ9xB8819jpxC9K5H0DsU37/e6sN6ZyPWOBDTkKzLEybJaMsSrKKTeUHjHEX60pECFpLepHNKXVbyUdQ9Jxzf/NXZKUe9Wl9s91jvvekcCplbyLkn4eztSL+p1KcB5fOfKtOldMDoXJ81QOFXdQ/HJf42dQvWuRNA7FN+819ipE+udiVzviJIHVsZyYZu5z2MytxVrOLzgCL9m5UaE9DBMXVI8ly/QLjulqnsoPvmvsVOo3pUIejdj+skn7zV26sR6ZyLXO6LE5Qb1TIZYNZCxP0QqUJgzm3K8leHfGsPzAz6qTxXPzYhtiuyUqu6h+OS/xk6helci6B2Kb95r7NSJ9c5ErndEiWtjwpdWvpGhHebnvrfyc6QChbc0Fl3G5fOQhE1FSg/ApQsr5/2murhz1dE70mzgSFX3UHzyX7vRJUTvSgS9Q/HNe42dOrHemcj1rqXAGPDBfCsgjqsl3yN+LJD8baouQz/VeXMOyxsNRtuR51FAihYZcN5D/owD+JcuSq8AvQT4tcZw40K8l6VQ7Yvek5Hz65SpLiLtSw9k2tF7WFPYKUXdm4Um/7V2Sk3vVpdbHzux3rWJPlFqXP5t5NyC90x1pba/zvcjYuj82zs/xwWfTPihXszocUpeEgsF6WsO7znZQ6MUHnKky/9OsNPJDi9PrHctAosDs/L3rDSmPgzKC+BBwRtxUoZZWd7JhcGp/9uA/8fHhltjjYxmPqKdaCfaKSk7ReWElSdWjsnnY/L5hEccmBPDCvKHVr6u88xNaaizYKPA2/L3GZlu6Wd5IIQQP9AIv58LuyLhGuBqsyx/vyKNsYvaNl1Ml2CRZN4cnlO/Y8rn2AkhpJtodHPSIYqOodTM9aD3/LupzmHXgM/oqOPZjYxi25meeA2MAkaYr4QQ4kdRY605axjTJfn5dLjm5K87yu7ugp8nFlWxQHIm8/1uhDcZhUKhpCDR0Eyf1Oa+XYwa946tN03VrTALttLmdzphOud2pnHnllZCCKdWPF4C2gVNfP+nObxTq8ZaQcJ5N0S8DOZzv//AHPZQ2TYHC66EEEJKgP/2NeWzmDqZzYXBxeargt/gLODssZWurbTzud7+vPF3eySEkJ4EuyaxMUe76adPnh+Wz9iJCZ/x4wW/mc419Ng2W1vcxOaAdyXO7Mlp2M770srn5mAHJ0YCE9LIjzPrCCGkyo+mscn62qlfi6b8RhScebCR+fwyE8+u9NiHHL+D1wp8y7fk2X9M9cCdS8w20gKyU4PrpjEvqmbEQQghJBCMQuF59ajNcRBCCAlkN5E4CCGENADcaFcTiIMQQnoGrNsU+dzmryArAgv6mN8eDtCnGXEQQkjPAA+qJwUNORYcHyvjwm7jZRN2w0wz4iCEkJ4CO5CnCxpyHNZ2X9mLxm02A4E98dA4CCGkp8A1W7XjH+o15DgTCLfWYGPbc1NdgFxx9JjRAI8qRwA4XgL3U8LNEK65g55xEEIIMQcX7Z4uacix9wHHK1+XBhdz5XcdvXTNORdoxOFSeEt63dABO5InPOIghBAi4FaamVxD7AKb087mwtAIbzWY5j2anhBCwsHxy+uOHnUe9L53HOFHG2jIEdemKb4EnBBCiJLfzP+3v7sachyhvOIIx81WDz3TvGDaeEM6IYR0G9oznHHC5oLj9zj984ZnmjjzZ4mmJ4SQuI17HtcRyrVFUl8/7/NWntLMhBDS2oYcPWgsdtaOQR6SsKkG08Dxy/BYwcUpWDDFheFjND0hhMRryF9YuSyN+b40xJMBaeCi8VWJC736aZqdtJJ/ATrx/Ubi0oaHAAACL3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj4mI3gyNUIzOzwvbWk+PG1pPkE8L21pPjxtaT5CPC9taT48bWk+QzwvbWk+PG1mcmFjPjxtcm93Pjxtbz4oPC9tbz48bWk+YTwvbWk+PG1vPis8L21vPjxtaT5iPC9taT48bW8+KzwvbW8+PG1pPmM8L21pPjxtbz4pPC9tbz48bW8+KDwvbW8+PG1pPmI8L21pPjxtbz4rPC9tbz48bWk+YzwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bWk+YTwvbWk+PG1vPik8L21vPjxtbz4oPC9tbz48bWk+YzwvbWk+PG1vPis8L21vPjxtaT5hPC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5iPC9taT48bW8+KTwvbW8+PG1vPig8L21vPjxtaT5hPC9taT48bW8+KzwvbW8+PG1pPmI8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmM8L21pPjxtbz4pPC9tbz48L21yb3c+PG1yb3c+PG1uPjQ8L21uPjxtc3VwPjxtaT5iPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtc3VwPjxtaT5jPC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mcmFjPjxtbz49PC9tbz48L21hdGg+FSWxngAAAABJRU5ErkJggg==)
Hint:
We will discuss the properties of triangle formulae which will help us to solve
of problems on triangle.
The correct answer is: ![S i n squared space A](data:image/png;base64,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)
In any ![straight triangle A B C fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis over denominator 4 b squared c squared end fraction equals](data:image/png;base64,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)
S =
{ semi-perimeter }
![left curly bracket left parenthesis a plus b plus c equals 2 s comma left parenthesis b plus c minus a equals 2 s minus 2 a space comma c plus a minus b equals 2 s minus 2 b space comma a plus b minus c equals 2 s minus 2 c space right curly bracket
fraction numerator left parenthesis 2 s right parenthesis left parenthesis 2 s minus 2 a right parenthesis left parenthesis 2 s minus 2 b right parenthesis left parenthesis 2 s minus 2 c right parenthesis over denominator 4 b squared c squared end fraction equals space fraction numerator 4 left parenthesis s right parenthesis left parenthesis s minus a right parenthesis cross times left parenthesis s minus 2 b right parenthesis left parenthesis s minus 2 c right parenthesis over denominator open parentheses b c close parentheses open parentheses b c close parentheses end fraction
bold space bold left square bracket bold space bold space bold italic W bold italic e bold space bold italic k bold italic n bold italic o bold italic w bold space bold italic t bold italic h bold italic a bold italic t bold space bold italic s bold italic i bold italic n bold space bold A over bold 2 bold space bold equals bold space square root of fraction numerator bold left parenthesis bold s bold minus bold b bold right parenthesis bold left parenthesis bold s bold minus bold c bold right parenthesis over denominator bold b bold c end fraction end root bold comma bold space bold space bold italic c bold italic o bold italic s bold space bold A over bold 2 bold space bold equals bold space square root of fraction numerator bold s bold left parenthesis bold s bold minus bold a bold right parenthesis over denominator bold b bold c end fraction end root bold space bold right square bracket
fraction numerator 4 left parenthesis s right parenthesis left parenthesis s minus a right parenthesis cross times left parenthesis s minus 2 b right parenthesis left parenthesis s minus 2 c right parenthesis over denominator open parentheses b c close parentheses open parentheses b c close parentheses end fraction bold space equals bold space 4 cross times s i n squared space straight A over 2 space cross times c o s squared space straight A over 2 space
left parenthesis bold space 2 cross times s i n space straight A over 2 space cross times c o s space straight A over 2 space right parenthesis squared space space space space space space space space space space left curly bracket W e space k n o w space t h a t space colon space 2 cross times s i n space straight A over 2 space cross times c o s space straight A over 2 equals space sin space A space right curly bracket
sin squared 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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.
Related Questions to study
In ![straight triangle A B C sum a cubed Sin space left parenthesis B minus C right parenthesis equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALcAAAATCAYAAADS45xnAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABGBJREFUeNrtW39EXVEcv54kMyPzzCSRJP0xsT9mkonM5P0xkXmSSWSSmcRkksxIksn+yTzZHxOZZDIjkzzTP5lk+mP0x6Q/MpI8efJo52yfq7Ozc849595zrlfuhy/dH+/ec77fz/n+OjfPu3w4iygJEiTklrz3lMgWkfuJKRLYRj9DtJkQBLWBJiI/y0Qfg0Qmy9xmkxhnAg1Qr3kMsn4kUhUzuVNEDstAD7eIbFwQm33FeGNDB5EikfYIz3gWcJ0+vwRPtwsy3hTcV09kCiH/BPe/JFIteW4zkX0QdpNIOiadXSfyhkifgPCviBwgdckTyThcYD5hWiLq3RaC7HcbOokF1BjbIPg2jk3xCIaskFxvwGRZ0AnPc+dGiKwQaWPGUYuFM694/w0QmxJmD4SPI9/vFVybJjIMXVDpIrLmkNwtIHcUvduCrv3yILlzUENM4O8JDNAE1VgUq0QeSu6h599z57q4c8+JvI0wjyvwSpQ0RzEUetfgoQe484WYwzz1kkMR9G4LJvZ7Gkd9QEPrDojhE2QH53UxRyRL5DHCtAjjmDyLd0Qe4O9GhMwKC3OaAcFLKDpNo9gEk1JQr1enkW6xoGG4NUTe7x93Qxf0uevwfCp8hqcMo3dbMLXfXSJfXJObErOHO5fFed1BrjCpwa7kvkV4kRTCaI7L0ac1cnZdZJm0IWf4WzqXWUSjFDNuGdqQDvFdnAJIVWlI7m54Yn9B9YHgKhwr3hOkd1swtV8lxq1K+SK1cVW5mk5FWwHDsp7lm/e3PcbjBzOwgsBz7CA/jIpmpnuyadA98RfFosDLdUqUX4TXFHn2DEi5r0gZRORuF0SS04BxlxTXgvRuC2Hsd+o5hIrAKuKzIY/Pz2kOOigwUIFZsR1oWzUy14sW5nOVMeahRjjnsYZIxGJdIy0JWjBHmG9aMy0xLTxLihRLpXdbHjOs/ZyRWyf18HNpEZrgpXncQ1HH4o4gv+pB+A0KUSZYZowQppg84TpFKUvFIX3OKMbngtyytCRI77YQxn7O0hLdopFe/y4J7XnFi/mWYFaQ+/ZylXWBKWrDVur++8dDPuMXd9wqWcBhCV50RO5VSQGro3dbMLWfs4KS9jmHNe8d8c7bhD5o6+u14jcLXJ466/2/0ZHjokLOM29BstHCJ/ZKBL3scwt5jMgHSzqnBeqeI3LLWoE6ercFU/sNOYggf3aPtjz9jZoU7q/HMd3Z2kZ+K0M/R/4lppBJoyOwxYXSOuTJo975TlYVCrMc8kURatC2O0Onpjriop/DnOl4aC/4U4jn5EGqGhzXYtENOCK3rD7S0bstmNrPySbOshfuC7olprWUCXhHDQo7H4dch2GBMTyLBnQn/G7HETxnp6Jbs4F7Tzyz7xVkhHmBOY7BOAcBrUBZyF3CXP3t9y7NbkkYcnvQAz9/Xb3bgq79Yt1+v6iYY4zXY/hb3a3v9AXRRfLh1CVD8s8K/+KJV/6fvE4J0rMECbkTyPAbh3euiEum0W8AAAETdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDI1QjM7PC9taT48bWk+QTwvbWk+PG1pPkI8L21pPjxtaT5DPC9taT48bW8+JiN4MjIxMTs8L21vPjxtc3VwPjxtaT5hPC9taT48bW4+MzwvbW4+PC9tc3VwPjxtaT5TaW48L21pPjxtbz4mI3hBMDs8L21vPjxtbz4oPC9tbz48bWk+QjwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bWk+QzwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48L21hdGg++84DkgAAAABJRU5ErkJggg==)
In ![straight triangle A B C sum a cubed Sin space left parenthesis B minus C right parenthesis equals](data:image/png;base64,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)
If
then ![s i n to the power of 2 end exponent invisible function application A plus s i n to the power of 2 end exponent invisible function application B plus s i n to the power of 2 end exponent invisible function application C equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALUAAAARCAYAAACb3u1RAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAtxJREFUeNrtWb9LHEEYHQ45JEhARIIcIgSRK9MESRGuuUJERAQJixwShBQpQoqAhBRXhDRiISGNyHFYiCByhYiNBBEJaUTEIoVgkX8gBDmOIxxcvo+81WHYH7djdvd2bh+8YmdnduftfDPfjxUiGrTBP8RvxHFhPnpJcy+u7y0yxNfE81RzqtU0NFPNqVaTUCCepJpTrd2EBtyMDkYQcz3usP/bHtHMJ1uL+JN4TdzHOFPXl++vEi/wPtb9kTgYh2BOAC41x04QDwIs1gskHn0xG3TYmsexuDJ4gauGru879HsubZ5RHGBVkSCw0EPiww77D+LjHhHnNDLxJGlmfdtK27xDmwlaV4ibUU/uA1xBCx9sRblfVtrK2HmPsMvYlfwivlHGseB8gHlsEC3iEvFLyEYdt+aywzu3iFOGaZ1AaNUXtUHzLsp69NlVTs5dCKwiQWB3kkOM+ED5+Crd8AzuSeBjXodo1N2g2X4+P+cJsRIgl0iS1jXNHKndAV3BAX7R5wVXECVfv3Lox7t5SEMA7+IzxFg2zgOe8kEWuhs0X0mLU+/whE6i1h8ihp8yCzCgWZf7Gbgf+bruYpgNzTnY7k7GJ/GvoB/GTo5bs/y8LIzuO1y1SVozIsbaNQf8p8Rj4oBybxLtbtdy+HCs8e68cP4TVUCJK6yYOk7N/LyvStsiyl0maeUNe6Npk/cKP2z0o/JQUtotpeRiuZRgLM3SzKnHpIOU9nQqAnFpthBDyygFqBAkSWtdicMjRwUnhozPxGWPa792L3Dctu5xf4c4HXJJL2rN9riXDvOwDNRacQgtI8NTBPVqIlBTDKvmYmi1AAZou8RLB3coY9nH6O+70FFrlsfZieEw4t4LnwpFUrWOIcF8L+7+HLLXmIHBF/+3If/GB2ohXsq7ZLz9Htd+7V5lpBmfPjlk4qZolsfZIVYTHikXwkHVDVoFqh9biK/bmNee5iZJkaJ38Bc3M0IDLOcmdAAAAXR0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bXJvdz48bWk+czwvbWk+PG1pPmk8L21pPjxtaT5uPC9taT48L21yb3c+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjA2MTs8L21vPjxtaT5BPC9taT48bW8+KzwvbW8+PG1zdXA+PG1yb3c+PG1pPnM8L21pPjxtaT5pPC9taT48bWk+bjwvbWk+PC9tcm93Pjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeDIwNjE7PC9tbz48bWk+QjwvbWk+PG1vPis8L21vPjxtc3VwPjxtcm93PjxtaT5zPC9taT48bWk+aTwvbWk+PG1pPm48L21pPjwvbXJvdz48bW4+MjwvbW4+PC9tc3VwPjxtbz4mI3gyMDYxOzwvbW8+PG1pPkM8L21pPjxtbz49PC9tbz48L21hdGg+AXcsFAAAAABJRU5ErkJggg==)
If
then ![s i n to the power of 2 end exponent invisible function application A plus s i n to the power of 2 end exponent invisible function application B plus s i n to the power of 2 end exponent invisible function application C equals](data:image/png;base64,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)
If
then ![c o s to the power of 2 end exponent invisible function application A plus c o s to the power of 2 end exponent invisible function application B plus c o s to the power of 2 end exponent invisible function application C equals](data:image/png;base64,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)
If
then ![c o s to the power of 2 end exponent invisible function application A plus c o s to the power of 2 end exponent invisible function application B plus c o s to the power of 2 end exponent invisible function application C equals](data:image/png;base64,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)
In ![straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM4AAAATCAYAAADYvzI1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABFpJREFUeNrtW1FkHUEUXc8TUf2JioioEhGRjwr9qKqKEFVRVaXqiaoKVRVVESoqIqpEVFT0J+KJflSIiqioEhURkZ+qiMpHyUdVPqJEVETE4/WOnpXpdGZ3ZndmXiN7OLy3O7tv7p1779x7d18QnAyUUzJDhhOJzHEyZEiAHs4JxhI4XVo8Io5ky1ARjED/GRLiKvEXHOE9sdqT45wnrmbqryhWsA7e0Ek8IHakuMeTmPPs/iXid+ImjLpeMq6ROEpcI+5j/HNijcFcWolbcIbPxFpPi9ZWgV0uqZ5dp8wuEGcbF4jLvoTMEdfhPOv4boo7xENiXnG+CcLyYAJPCcf6ifPEK9w8zsIppwznVAenYYv4A87kCm1wnEobmK6ej6Pj6NrGMhzIOfqIw/g8jAmaoAYOt0C8qRjDjr8Vjt0Sjj0lTlqW7RQiLlvIXaRxLsCiYO9/kKro6Pk4wsQ2HvuoM88QN2BgoaFt4LguJogF4j3ia8WYIQjP4w3xGj43I63IO5JzDM5TQgPBdEdmAWUbuyqL6OeEMR8RCcW0YhEphaprV1Z8vw19sLRrCZFVB3F6tpUu+ZTL1DYuET+5dhxm9N3CsQKO605ynkuNNhXjZhANc0hrikJN9FKjRkqDArfIRcNrmXzj2FlznCw8WDOiSjjG0sQbhilNGcY1yjnnfRiZDuL0bAO+5TK1jSqsh2peqR9JROXlOt2JPJTIR40vxBbJ2G/cxPYkEXAD+bkLtAZHXTY232pDh5uRRPAu4VhJcu2+RkNDZmAdkh3vUHO+cXq2Ad9yJbGNw8AhopxDp9gdktRDL4J/e+k5LGIYDVgTYhVbcHj+wJGMpzlj2jFIeUIsYlflsSRJ1UqKemMFzmdiYEmL7Tg924q+PuVKahvOHEcnHZuIUE4LdhcR7SjGeVyU5Jzd2Lbjtta0mOOMIEljYD/4u8vIG2dcqhY67iSiZrNjx4nTs+2A5EOuJLbhLFXTbQCw818Vqc1yxA+LbemCpK64K3RJ9rgGhc1OTDinoYT3+Cl8v6wIGAs4p8KA4jqbjqOjZ9vwIZepbThrDrC+fp/m2P7gqFUd4gHxVcQ100INMI5CkEdR2M2KgXkbPArtnNPMp7jPlhA4BonvJOPi2tGqfN6mgeno2TZ8yGVqG70udlnWSlwL9B9y5jC+Ed/ZE+h1bNUq9AiONcsVqbXorqwJqc051CADXOHJDPY6FNcpOGY5UD8zagj+tI7L6PLVpAwyE9ADmyN7HvIhQU3Yg3rJpYHp6Nk2fMhlYhthNmT9AehckOyt4VlcP4MJR6EBBXmIHe4+BzD8Bsl1TehYhR2wXUT3LsmOpnKcPAriMuoTk/eWVIv4DHIPYsG2Fb+9KvxeKHMJzlbv2MB09ZwWvuUysQ2vr9wcR0xLlBY2NMKF7U5gEDpQvfeWveRZeXh/yfM4oQ1Ni3zCronL/+M8DLK/FVQKo6i/M0SkgnUxaUT2R7YMVvAbqJ7Nr5nKDI0AAAEhdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDI1QjM7PC9taT48bWk+QTwvbWk+PG1pPkI8L21pPjxtaT5DPC9taT48bW8+LDwvbW8+PG1vPiYjeDIyMTE7PC9tbz48bWk+YTwvbWk+PG1vPig8L21vPjxtaT5zaW48L21pPjxtbz4mI3hBMDs8L21vPjxtaT5CPC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5zaW48L21pPjxtbz4mI3hBMDs8L21vPjxtaT5DPC9taT48bW8+KTwvbW8+PG1vPj08L21vPjwvbWF0aD6lOl5HAAAAAElFTkSuQmCC)
The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.
In ![straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals](data:image/png;base64,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)
The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.
The perimeter of a Δ ABC is 6 times the A.M of the sines of its angles if the side "a" is 1, then the angle A is
The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.
The perimeter of a Δ ABC is 6 times the A.M of the sines of its angles if the side "a" is 1, then the angle A is
The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.
The resistance of a resistance thermometer has values 2.71 and 3.70 ohm at 10ºC and 100ºC The temperature at which the resistance is 3.26 ohm is
The resistance of a resistance thermometer has values 2.71 and 3.70 ohm at 10ºC and 100ºC The temperature at which the resistance is 3.26 ohm is
Diborane is a Lewis acid forming addition compound
with
, a Lewis base. This
Diborane is a Lewis acid forming addition compound
with
, a Lewis base. This
If the angles of triangle are in the ratio 1:1:4 then ratio of the perimeter of triangle to its largest side
if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c .
If the angles of triangle are in the ratio 1:1:4 then ratio of the perimeter of triangle to its largest side
if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c .
The pressure on a swimmer 20 m below the surface of coater at sea level is
The pressure on a swimmer 20 m below the surface of coater at sea level is
can’t be stored in
can’t be stored in
The angles of a triangle are in the ratio 3:5:10. 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.
The angles of a triangle are in the ratio 3:5:10. 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.
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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)
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)