The rhombus side ABCD is 24 cm and the angle A is 30 °. Find the distance from the vertex B to the opposite side AD?

Let us designate the distance from vertex B to the opposite side of AD as ВK.

1) What is the area of the diamond ABCD?

Since all sides of the rhombus ABCD are equal, then AD = 24 cm, hence

S = AD ^ 2 * sin A = 24 ^ 2 * sin30˚ = 576 * (1/2) = 576/2 = 288 (cm ^ 2).

2) What is the distance from vertex B to the opposite side AD?

In order to find ВC, we use the formula S = BK * AD, we have

ВK = S: AD = 288: 24 = 12 (cm).

Answer: the distance from vertex B to the opposite side AD is 12 cm.