Question

If two sides of a triangle are given, then the area of the triangle will be maximum, if the angle between the given sides is

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

Answer 1

Answer: (D)

$\frac{\pi }{2}$

Let $a$ and $b$ be given, the area, $A=\frac{1}{2}ab\sin C$
$\Rightarrow \frac{dA}{dC}=\frac{1}{2}ab\cos C$
Hence, $A$ is maximum, when $\frac{dA}{dC}=0$
$\Rightarrow C={90}^o=\frac{\pi }{2}$