In an isosceles triangle, the angle is C = 30, AC = BC = 72. Find the height AH.

Given:

triangle ABC – isosceles,

AC = BC = 72 cm,

angle C = 30 °.

Find: AH -?

Decision:

Let us omit the height AH in triangle ABC.

Consider a triangle ACH, it is rectangular (since AH is the height, so the angle AHC = 90 °), in which CH and AH are legs, and AC is the hypotenuse.

By condition, it is known that: angle C = 30 °, AC = 72 cm.

By the property of a right-angled triangle: a leg lying opposite an angle of 30 ° is equal to half the hypotenuse, therefore:

AH = 1/2 * AC = 1/2 * 72 = 36 cm.

Answer: 36 cm.