In a regular triangular pyramid, the side of the base is 12 and the height is 10√3. Find the tangent of the angle

| September 9, 2021 | education

In a regular triangular pyramid, the side of the base is 12 and the height is 10√3. Find the tangent of the angle of inclination of the side face to the plane of the base.

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 = 12/2 = 6 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 = 144 – 36 = 108.

CH = 6 * √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 = 6 * √3 cm.

3 * OH = 6 * √3.

OH = 2 * √3 cm.

In a right-angled triangle DOH tgDNO = DO / OH = (10 * √3) / (2 * √3) = 5.

Answer: The tangent of the angle between the side face and the base of the pyramid is 6.



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