Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

If the sides of a triangle are in the ratio $x colon y colon square root of x squared plus x y plus y squared end root$ then greatest angle is

$90^{\circ}$
$120^{\circ}$
$\cos^{- 1} (\frac{x + y}{x - y})$
$60^{\circ}$

hint Hint:

In this question, we have to find the angle of the greatest angle. As c is the greatest side so angle C is the greatest angle. As we know the sides ratio, so using the cosine formula we will find the angle of the greatest side.

The correct answer is: $120 to the power of ring operator$

As the ratio of the sides is $x colon y colon square root of x squared plus x y plus y squared end root$
a= x, b=y, c = $square root of x squared plus x y plus y squared end root$
c is the largest side, so, C is the largest angle.
$cos space C space equals open parentheses fraction numerator a squared plus b squared minus c squared over denominator 2 a b end fraction close parentheses space space space space space space space space space space space equals open parentheses fraction numerator x squared plus y squared minus open parentheses x squared plus x y plus y squared close parentheses over denominator 2 x y end fraction close parentheses space space space space space space space space space space space equals open parentheses fraction numerator x squared plus y squared minus x squared minus y squared minus x y over denominator 2 x y end fraction close parentheses space space space space space space space space space space space equals fraction numerator negative x y over denominator 2 x y end fraction space space space space space space space space space space equals fraction numerator negative 1 over denominator 2 end fraction rightwards double arrow cos space C equals cos space 120 degree rightwards double arrow C equals 120 degree$
So, the angle of the greatest angle is 120 $degree$ .

Related Questions to study

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open square brackets fraction numerator a to the power of 1 over x end exponent plus b to the power of 1 over x end exponent plus c to the power of 1 over x end exponent over denominator 3 end fraction close square brackets to the power of x$ where are real and non-zero=

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open square brackets fraction numerator a to the power of 1 over x end exponent plus b to the power of 1 over x end exponent plus c to the power of 1 over x end exponent over denominator 3 end fraction close square brackets to the power of x$ where are real and non-zero=

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x squared plus 5 x plus 3 over denominator x squared plus x plus 2 end fraction close parentheses to the power of x equals$

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x squared plus 5 x plus 3 over denominator x squared plus x plus 2 end fraction close parentheses to the power of x equals$

In $straight triangle A B C text , if end text c squared equals a squared plus b squared comma 2 s equals a plus b plus c text then end text 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals$

In $straight triangle A B C text , if end text c squared equals a squared plus b squared comma 2 s equals a plus b plus c text then end text 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals$

parallel

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus 6 over denominator x plus 1 end fraction close parentheses to the power of x plus 4 end exponent equals$

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus 6 over denominator x plus 1 end fraction close parentheses to the power of x plus 4 end exponent equals$

If tan $A plus tan invisible function application B plus tan invisible function application C equals 3 square root of 3$ then the $straight capital delta to the power of k$ is

If tan $A plus tan invisible function application B plus tan invisible function application C equals 3 square root of 3$ then the $straight capital delta to the power of k$ is

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 5 over denominator x plus 2 end fraction close parentheses to the power of x plus 3 end exponent equals$

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 5 over denominator x plus 2 end fraction close parentheses to the power of x plus 3 end exponent equals$

parallel

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent equals$

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent equals$

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of x minus e to the power of s in space x end exponent over denominator 2 left parenthesis x minus sin space x right parenthesis end fraction equals$

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of x minus e to the power of s in space x end exponent over denominator 2 left parenthesis x minus sin space x right parenthesis end fraction equals$

If the sides of triangles are then radius of the Circumcentre is

If the sides of triangles are then radius of the Circumcentre is

parallel

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator open parentheses 1 minus e to the power of x close parentheses sin begin display style space end style x over denominator x squared plus x cubed end fraction equals$

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator open parentheses 1 minus e to the power of x close parentheses sin begin display style space end style x over denominator x squared plus x cubed end fraction equals$

The function $f left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript fraction numerator d t over denominator t end fraction$ satisfies

The function $f left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript fraction numerator d t over denominator t end fraction$ satisfies

$text If end text a greater than 0 text and end text L subscript x not stretchy rightwards arrow a end subscript fraction numerator a to the power of x minus x to the power of 4 over denominator x to the power of x minus a to the power of a end fraction equals negative$ 1, then a=

$text If end text a greater than 0 text and end text L subscript x not stretchy rightwards arrow a end subscript fraction numerator a to the power of x minus x to the power of 4 over denominator x to the power of x minus a to the power of a end fraction equals negative$ 1, then a=

parallel

If a,b,c are in A.P then $c o t A over 2 comma c o t B over 2 a n d space c o t C over 2$ are in

If a,b,c are in A.P then $c o t A over 2 comma c o t B over 2 a n d space c o t C over 2$ are in

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x left parenthesis 1 plus a cos invisible function application x right parenthesis minus b sin invisible function application x over denominator x cubed end fraction equals 1 text then end text straight a equals comma straight b equals$

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x left parenthesis 1 plus a cos invisible function application x right parenthesis minus b sin invisible function application x over denominator x cubed end fraction equals 1 text then end text straight a equals comma straight b equals$

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x 10 to the power of x minus x over denominator 1 minus cos space x end fraction equals$

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x 10 to the power of x minus x over denominator 1 minus cos space x end fraction equals$

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.