In a regular hexagonal pyramid, the side faces make an angle of 60 ° with the base plane

In a regular hexagonal pyramid, the side faces make an angle of 60 ° with the base plane. Find the tangent of the angle between the base plane and the side edge.

Given: H = 60 °

Find: tg <=?

Decision:

1. We need to draw a hexagon lying at the base of the pyramid, then we need to inscribe a circle there, its radius will be = X

2. We see a right-angled triangle with legs X and H, from angles of 60 °

3. Make up the ratio: H = X * tg = X * √3

X = 2X \ √3

H = X * √3

4.tg = X * √3 \ (2X \ √3) = 3 \ 2 = 1.5

Answer: tg = 1.5