# The segment AM is perpendicular to the plane of the triangle ABC and has a length of 24 cm

May 31, 2021 | education

| **The segment AM is perpendicular to the plane of the triangle ABC and has a length of 24 cm. Find the distance from point M to the straight line BC, if AB = AC = 20 cm, BC = 24cm.**

Let’s write it down briefly:

triangle ABC;

AB = AC = 20 cm;

BC = 24 cm;

MA = 24 cm.

Find: MH -?

Decision:

Let’s first of all draw the height AH, it is also the median, since the triangle is isosceles, therefore:

СН = ВН = ВС / 2 = 24/2 = 12 cm.

we carry out the MN, the resulting triangle ANS is rectangular.

We apply the Pythagorean theorem and write:

AH = √ (AC ^ 2 – CH ^ 2) = √ (400 – 144) = 16 cm.

The AMN triangle is also rectangular, we do the same:

MH = √ (AM ^ 2 + MH ^ 2) = √ (576 + 256) = 8√13.