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?

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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?

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Answer 1 · 2016-01-22T09:44:31

Compute a median from the tip of the pyramid $m e d i a n = 2 \sqrt{3}$ $median=2sqrt(3)$ to the midpoint of any base. Use the radius $2$ $2$ of the square base as adjacent side. Angle $= {cos}^{- 1} (\frac{2}{2 \sqrt{3}})$ $=cos^-1 (2/(2sqrt3))$ $= 54.7356$ $=54.7356$ degrees

Explanation:

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

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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?

1 Answer

Explanation:

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