Question

The angle at the vertex of a cone is measured using a 30mm diameter coin as shown in the figure below. If the coin lies 3.72mm below the top of the cone, determine the value of angle θ.

Answer 1

diameter = 30mm

radius = 15mm

To find the value of $\theta$ .

we use identity tan$\theta$ = P/B

P = perpendicular

B = base

P = 3.72mm and B = 15mm

tan$\theta$ = 3.72/15

tan$\theta$ = 0.248

$\theta$ = tan^-1(0.248)

13.92834

=13.93°

The angle at the vertex=(90-13.92)*2=152.14°