How do you solve this problem?

Question

Two sides of a triangle have lengths a and b and the angle between them is angle theta. What value of angle theta will maximize the triangle's area? Use the formula A=1/2absintheta.

Answer 1

Given, the area of a triangle A = ½ ab sinθ where a and b are the sides and θ is the contained angle.

Now, to maximize the are of the triangle, we need to find it's critical points by setting A' = 0

A' = ½ ab cosθ

0 = ½ ab cosθ

θ = π/2

Thus at angle θ = π/2, the area of the triangle is at it's maximum