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  • Stuck here, help me understand: - In a triangle, the sum of lengths of two sides isand the product of the lengths of the same two si - Trigonometry - JEE Main

In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y.

If x^{2}-c^{2}=y, where c is the length of the third side of the triangle, then the circumradius of the triangle is :

  • Option 1)

     

    \frac{y}{\sqrt3}

  • Option 2)

     

    \frac{c}{\sqrt3}

  • Option 3)

     

    \frac{c}{3}

  • Option 4)

     

    \frac{3}{2} y

Answers (1)

best_answer

 

Allied Angles -

- wherein

The trigonometric ratios for angles in all the four quadrants.

 

 

Trigonometric Ratios of Special Angles -

- wherein

These are the values of trigonometric ratios for standard angles. 

 

 

Let a,b,c be 3 sides of trangle

a+b=x

ab=y

\Rightarrow (a+b)^{2}-C^{2}=ab

\Rightarrow \frac{a^{2}+b^{2}}-c^{2}{2ab}=-\frac{1}{2}

\Rightarrow \cos C=-\frac{1}{2}\Rightarrow C=\frac{2\pi }{3}

Circumradius , \frac{c}{\sin c}=2R

\Rightarrow \frac{2c}{\sqrt{3}}=2R

\Rightarrow R=\frac{C}{\sqrt{3}}

 

 


Option 1)

 

\frac{y}{\sqrt3}

Option 2)

 

\frac{c}{\sqrt3}

Option 3)

 

\frac{c}{3}

Option 4)

 

\frac{3}{2} y

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