In a regular triangular pyramid, the base side is 10 and the height is 5. Find the angle between

| September 7, 2021 | education

In a regular triangular pyramid, the base side is 10 and the height is 5. Find the angle between the side face and the base of the pyramid.

The base of the regular pyramid is the equilateral triangle ABC. The height of the CH, drawn to the side AB, is also the median of the triangle, then BH = AH = AB / 2 = 10/2 = 5 cm.

In a right-angled triangle BCH, according to the Pythagorean theorem, we determine the length of the leg CH.

CH ^ 2 = BC ^ 2 – BH ^ 2 = 100 – 25 = 75.

CH = 5 * √3 cm.

By the property of the medians, the point of their intersection divides the medians in the ratio of 2 / 1. Then CO = 2 * OH.

CH = CO + OH = 5 * √3 cm.

3 * OH = 5 * √3.

OH = 5 * √3 / 3 cm.

In a right-angled triangle, DON tgDNO = DO / OH = 5 / (5 * √3 / 3) = 3 / √3 = √3.

Angle DNO = arctg√3 = 60.

Answer: The angle between the side face and the base of the pyramid is 60.



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