Through the vertex A of the triangle ABC, a straight line AM is drawn perpendicular to the plane

Through the vertex A of the triangle ABC, a straight line AM is drawn perpendicular to the plane of this triangle. It is known that AM = 15, BC = 12, AB = AC = 10. Find the distance from point M to line BC.

In the triangle ABC, we will build the height of AH to the base of the BC. Since triangle ABC is isosceles, its height AH is also its median.

Then ВН = СН = ВС / 2 = 12/2 = 6 cm.

The ACN triangle is rectangular, then, according to the Pythagorean theorem, AH ^ 2 = AC ^ 2 – CH ^ 2 = 100 – 36 = 64.

AH = 8 cm.

Since AM is perpendicular to the plane of the triangle ABC, the triangle AMN is rectangular.

Then MH ^ 2 = AM ^ 2 + AH ^ 2 = 225 + 64 = 289.

MH = 17 cm.

Answer: From point M to straight BC 17 cm.