$\left.\frac{\text { [Inscribed and Circumscribed Circles ]}}{\text { Rhombuses Properties and Characteristics }}\right]$

The side of the rhombus is 8 cm, and the acute angle is $30^{\circ}$. Find the radius of the inscribed circle.
The diameter of the inscribed circle is equal to the height of the rhombus.

## Solution

The diameter of the inscribed circle is equal to the height of the rhombus, and the height, dropped from a vertex to the opposite side, is the leg of a right triangle opposite the angle of $30^{\circ}$.

Therefore, the height of the rhombus is 4, and the desired radius is 2.

![](https://cdn.mathpix.com/cropped/2024_05_06_845c09db4774ba28be39g-13.jpg?height=326&width=1403&top_left_y=886&top_left_x=333)

## Answer

2 cm.