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.

Question

Philoid · Accepted Answer

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,

Condition for maxima and minima is

So, for A to be maximum,

For

Hence, will give maximum area.

And maximum area will be