Given a rhombus, the side and the acute angle are known in degrees. Find the R of the incircle.

Given a rhombus, the side and the acute angle are known in degrees. Find the R of the incircle. Write the formula for finding the radius.

The area of a rhombus is equal to the product of the square of the length of its side by the sine of the acute angle between them.

Savsd = AB ^ 2 * SinBAD = a ^ 2 * Sinα.

Since the diameter of the circle inscribed in the rhombus is equal to the height of the rhombus, then the area of the rhombus will be equal to:

Savsd = AB * KH = a * D = a * 2 * R

Then: a * 2 * R = a ^ 2 * Sinα.

R = a2 * Sinα / 2 * a = (a * Sinα) / 2.

Answer: The radius of the inscribed circle is injured (a * Sinα) / 2.