At the base of the pyramid MABC lies a triangle ABC with AB = a and an angle of ACB

| May 26, 2021 | education

At the base of the pyramid MABC lies a triangle ABC with AB = a and an angle of ACB = 150 degrees. The side ribs are inclined to the base at an angle of 45 degrees. Find the height of the pyramid.

Since all the lateral edges are inclined at the same angle, the vertex D of the pyramid is projected to the center of the circle inscribed about the triangle ABC.

Triangle ABC is obtuse, then the center of the circumscribed circle, point O, lies outside the triangle.

By the sine theorem, R = AB / 2 * Sin150 = a / 2 * (1/2) = a see.

The projections of the side edges of the pyramid on the plane of the triangle ABC are the radii of the circumscribed circle, then the triangle AOD is rectangular and isosceles, since the angle OAD = 45.

Then OD = AO = R = a cm.

Answer: The height of the pyramid is a cm.



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