An isosceles triangle has an area A, an apex angle 2 theta, and a height of h. Determine an expression for theta in terms of A and h.

Answer 1

If the base of the triangle is 2b, then

b/h = tanθ, so
b = h tanθ

The area

A = 1/2 (2b)(h)
= bh
= h^2 tanθ

So, θ = arctan(A/h^2)