Find the angle formed between the line segments.

Question

c. Imagine two line segments where each represents a slant height of the cone. The segments are on opposite sides of the cone and meet at the apex.

Answer 1

Consider triangle ABV inside the cone, where VA and VB are the slant heights of the cone (at the opposite sides). AB=2r (r is the radius on the cone base), so AO = OB = r; VO=h (cone height); V is the apex of the cone;

We need the angle AVB = 2 angle OVA; tan (OVA) = r/h; OVA = arctan (r/h);

Therefore, the angle AVB = 2 arctan (r/h);

Using h=6; r=4, angle AVB = 2 arctan(4/6) = 67.4^o