The side face of a regular triangular pyramid makes an angle with the base plane, the sine of which is 0.2 √3

| July 7, 2021 | education

The side face of a regular triangular pyramid makes an angle with the base plane, the sine of which is 0.2 √3, and the side of the base of the pyramid is 10. Find the distance from the apex of the base of the pyramid to the plane of the side face.

Let’s draw the median АН of the triangle ABC, which is also the height and the bisector. Then CH = BC / 2 = 10/2 = 5 cm.

In a right-angled triangle ACH, AH ^ 2 = AC ^ 2 – CH ^ 2 = 100 – 25 = 75.

AH = √75 = 5 * √3 cm.

The distance from the top of the base to the side is a perpendicular drawn from point A to the height BH of the side face.

Then in a right-angled triangle AKH, SinАHК = AK / AH.

AK = AN * SinАHK = 5 * √3 * 0.2 * √3 = 3 cm.

Answer: The distance from the top of the base of the pyramid to the plane of the side face is 3 cm.



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