MathDB

How many distinct triangles

ABC

are tjere, up to simplilarity, such that the magnitudes of the angles

A, B

and

C

in degrees are positive integers and satisfy

\cos{A}\cos{B} + \sin{A}\sin{B}\sin{kC} = 1

for some positive integer

k

, where

kC

does not exceet

360^{\circ}

Problem Statement