The point is 65 cm from each of the vertices of the isosceles triangle. Find the distance from this point to the plane

| August 7, 2021 | education

The point is 65 cm from each of the vertices of the isosceles triangle.Find the distance from this point to the plane of the triangle if its base and side are 48 and 40, respectively.

Since the top of the pyramid, point D, is equidistant from the vertices of the triangle ABC, it is projected to point O, the center of the circumscribed circle around the triangle ABC.

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

The half-perimeter of the triangle is: p = (48 + 40 + 40) / 2 = 64 cm.

Then Sav = √64 * (64 – 48) * (64 – 40) * (64 – 40) = √589824 = 768 cm2.

Then R = ОВ = AB * ВС * АС / 4 * Saс = 40 * 40 * 48/4 * 768 = 25 cm.

In a right-angled triangle VOD, according to the Pythagorean theorem, OD ^ 2 = BD ^ 2 – VO ^ 2 = 4225 – 625 = 360.

OD = 60 cm.

Answer: From a point to the plane of the triangle 60 cm.



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