In a regular triangular pyramid, the side edge is 10 cm and is inclined to the base plane

univerkov | June 17, 2021 | education

In a regular triangular pyramid, the side edge is 10 cm and is inclined to the base plane at an angle of 30 find the height of the pyramid.

Since we have a regular triangular pyramid, we can build a right-angled triangle with the height of the pyramid, the side edge of the pyramid and a straight line at the base. In this right-angled triangle, the hypotenuse is the edge of the pyramid, and the height is the leg, which is opposite an angle of 30 degrees. And as we know that the leg, which is opposite an angle of 30 degrees in a right-angled triangle, is 2 times less than the hypotenuse, that is, 10/2 = 5 cm.
Answer: the height of the pyramid is 5 cm.

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