Question

Let A, B, C be three angles such that A = π/4 and tan B tan C = p. Find all possible values of p such that A, B, C are the angles of a triangle.

Answer 1

A + B + C =  π ⇒ B + C = 3π/4 ⇒ 0 < B,C < 3π/4

tanB tanC = p

Since B and C can vary from 0 to 3π/4,

Combining Eqs. (1) and (2), we get