In a triangular pyramid, the sides of the base are 7, 8, 9. The angle between the side and the base is 60

| June 27, 2021 | education

In a triangular pyramid, the sides of the base are 7, 8, 9. The angle between the side and the base is 60 degrees. Find the sides of the pyramid.

Since the side faces of the pyramid are equal, the point O is the center of the circumscribed circle around the triangle ABC.

Let us determine the semiperimeter of the triangle ABC, p = (7 + 8 + 9) / 2 = 12 cm.

By Heron’s theorem, we determine the area of a triangle.

S = √12 * (12 – 7) * (12 – 8) * (12 – 9) = √720 = 12 * √5 cm2.

Then the radius of the circumscribed circle is: R = OA = AB * BC * AC / 4 * S = 8 * 9 * 7/48 * √5 = 21/2 * √5 cm.

In a right-angled triangle AOD, the angle ODA = (90 – 60) = 30, then the leg OA lies opposite the angle 30, then AD = 2 * OA = 2 * (21/2 * √5) = 21 * √5 cm.

Answer: The length of the side is 21 * √5 cm.



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