Question

A Christmas decoration is in the shape of a square based pyramid. All edges in the pyramid have a measurement of 4cm how do you find the angle between a triangular face and the base?

Answer 1

Compute a median from the tip of the pyramid `median=2sqrt(3)` to the midpoint of any base. Use the radius `2` of the square base as adjacent side. Angle`=cos^-1 (2/(2sqrt3))` `=54.7356` degrees

Explanation:

The radius of the inscribed circle =`2` inside the square base.
The height of the pyramid `=2sqrt(2)` by using pythagorean theorem. Here are additional data. From any corner of the square base to its center the measurement `=2sqrt(2)`. From any midpoint of the edge of the square base to the center `=2`. You can also use Angle`=tan^-1((2sqrt(2))/2)=54.7356`