Question

If the lengths of the sides of triangle are $3,5$ , and $7$ , then the largest angle of the triangle is

• A. $\frac{\pi}{2}$
• B. $\frac{5 \pi}{6}$
• C. $\frac{2 \pi}{3}$
• D. $\frac{3 \pi}{4}$

Answer 1

Answer: (C)

Let $a=3, b=5, c=7$.
Then the largest angle is opposite to the longest side, i.e., $\angle C$.
Therefore, $\cos C=\frac{a^{2}+b^{2}-c^{2}}{2 a b}$
$=\frac{9+25-49}{2 \times 3 \times 5}=\frac{-1}{2}$
or $C=\frac{2 \pi}{3}$