The side of the rhombus is 10 dm, and one of its angles is 30 degrees, find the radius of the circle

univerkov | May 2, 2021 | education

The side of the rhombus is 10 dm, and one of its angles is 30 degrees, find the radius of the circle inscribed in the rhombus.

Let’s define the area of a rhombus through the length of its side and the angle between them.

S = AB2 * SinBAD = 10 ^ 2 * Sin300 = 100 * 1/2 = 50 cm2.

Now let’s use the formula for the area of a rhombus in terms of the radius of the inscribed circle.

S = 2 * AB * r = 2 * 10 * r.

Then 50 = 2 * 10 * r.

R = 50/20 = 2.5 cm.

Answer: The radius of the circle is 2.5 cm.

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