Question

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

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

Answer 1

The correct option is D $\frac{\pi }{2}$

Let a and b are given sides of a triangle, then area $A=\frac{1}{2}absinC\Rightarrow \frac{dA}{dC}=\frac{1}{2}abcosC$
Hence A is maximum, when $\frac{dA}{dC}=0\Rightarrow C={90}^{\circ }$