In an isosceles triangle ABC, angle A is 15 degrees AB is equal to BC is 6 cm Find the height dropped from the vertex A.

Since the sides AB and BC of this triangle are equal, they are lateral sides, therefore, the AC side is the base. The angles at the base of an isosceles triangle are equal, so ∠A = ∠C = 15 °. The sum of the angles of the triangle is 180 °, we can find the angle B:
∠В = 180 – ∠А – ∠С = 180 – 15 – 15 = 150 °.
Let AK be the height dropped from the vertex A, then in the triangle AKB AK and BK are legs, AB is the hypotenuse. Knowing that AB = 6 cm, AK is the leg opposite to the angle B, equal to 150 °, we can write:
sin B = AK / AB;
AK = AB * sin B = 6 * sin 150 ° = 6 * 0.5 = 3 cm.