Question

Two sides of a triangle have lengths ‘a’ and ‘b’ and the angle between them is θ. What value of θ will maximize the area of the triangle? Find the maximum area of the triangle also.

Answer 1

It is given that Two sides of a triangle have lengths ‘a’ and ‘b’ and the angle between them is θ. 

Let the area of triangle be A

Then, 

A = \(\frac{1}{2}\)ab Sin θ

Hence, 

θ = \(\frac{\pi}{2}\) will give maximum area. 

And maximum area will be A = \(\frac{1}{2}\)ab