Question

If the sides of a triangle are in the ratio $5:8:11$ and $\theta$ denotes the angle opposite to the largest side of the triangle, then the value of ${\tan }^2\frac{\theta }{2}$ is equal to

• A. $\frac{7}{3}$
• B. $\frac{3}{2}$
• C. $\frac{8}{3}$
• D. $noneofthese$

Answer 1

Answer: (A)

$\frac{7}{3}$

Sides are in ratio $5:8:11$

Let the sides be $5x,8x,11x$

$\therefore s=\frac{24x}{2}=12x$

${\tan }^2\frac{\theta }{2}=\frac{(s-5x)(s-8x)}{s(s-11x)}$

$=\frac{7x-4x}{12x-x}=\frac{28}{12}=\frac{7}{3}$