Answer to Question #259 in Trigonometry for Nick Humphries

Question

A cone has a slant side measure (m) and a semi-vertical angle 2(x). Prove that the measure r of the radius of the sphere inscribed in the cone is given by:
r = (m sin(4x))/2(1+sin(2x))

Answer 1

You have to draw a picture and look at the triangles. Then, write down the sin/cos of the angle at the vertex of the different triangles.