In an isosceles triangle ABC, the base of which is the segment AC, the outer angle at the apex A is 150 °.

In an isosceles triangle ABC, the base of which is the segment AC, the outer angle at the apex A is 150 °. Calculate the height drawn to the side of the triangle if AC = 38 cm.

Let CD be the height drawn to the side of the triangle ABC.

The angle CAB is adjacent to the outer angle BAE, the sum of which is 180, then the angle CAB = (180 – 150) = 300.

The ACD triangle is rectangular, the CD leg lies opposite the angle 30, then its length is equal to half the length of the AC hypotenuse. CD = AC / 2 = 38/2 = 19 cm.

Answer: The length of the heights is 19 cm.