Question

Two sides of a triangle have constant lengths a and b, and the angle between them is theta. What value of theta will maximize the area of the triangle?

so far i have the formula and the derivative.
A=.5absin(theta)
A'=.5abcos(theta)

then i set the derivative to zero in order to get the critical point, but i don't know how to solve it because if I divide zero by .5, it will just be 0.

0=.5abcos(theta)

can anyone help me get past this step? thanks.

Answer 1

If A' = 0, and a and b are fixed positive numbers, then cos (theta) = 0 and theta = 90 degrees.

The answer seems intuitively correect.