Find the area of a rhombus if its height is 10 cm, and the acute angle is 30 °.

The height of the rhombus is perpendicular to its side and is a leg in a right-angled triangle, in which the side of the rhombus is the hypotenuse, and is opposite to the sharp corner of the rhombus. The ratio of the opposite leg to the hypotenuse is the sine of the angle, which means:

h / a = sin 30 °.

Hence the side of the rhombus:

a = h / sin 30 ° = 10 / 0.5 = 20 cm.

The area of a rhombus is equal to the product of the lengths of its side and height:

S = a * h = 20 * 10 = 200 cm2.