The acute angle of the rhombus is 30 °. Find the height of the rhombus if its perimeter is 16cm.

1. The tops of the rhombus A, B, C, D. BH – height. ∠А = 30 °.

2. Let us denote the length of the rhombus side by the index “a”.

3. Considering that the lengths of the sides of the rhombus are equal, we calculate their length using the formula for calculating the perimeter (P):

P = 4a = 16;

a = 4 centimeters.

4. In a right-angled triangle ABH, the height BH is opposite an angle of 30 °.

Therefore, its length (according to the properties of a right-angled triangle) is half the hypotenuse. The hypotenuse in the indicated triangle is the side of the rhombus AB. Consequently

BH = a / 2 = 4/2 = 2 centimeters.

Answer: The length of the height BH is 2 centimeters.