Question

The sides of a triangle are in the ratio $5:8:11$. If $\theta$ denotes the angle opposite to the largest side of the triangle,

then $ta{n}^2\frac{\theta }{2}=$

• A. $\frac{1}{21}$
• B. $\frac{7}{48}$
• C. $\frac{7}{3}$
• D. $\frac{7}{12}$

Answer 1

The correct option is C $\frac{7}{3}$

$a=5k,b=8k,c=11k$

$cosc=\frac{a^2+b^2-c^2}{2ab}$

$=\frac{5^2+8^2-{11}^2}{2\times 5\times 8}$

$cosc=\frac{-2}{5}$

$\frac{1-ta{n}^2\frac{c}{2}}{1+tan\frac{c}{2}}=\frac{-2}{5}$

$\frac{1+ta{n}^2\frac{c}{2}-1+ta{n}^2\frac{c}{2}}{1+ta{n}^2\frac{c}{2}+1-ta{n}^2\frac{c}{2}}=\frac{5+2}{5-2}$

$ta{n}^2\frac{c}{2}=\frac{7}{3}$