Question

Сторона ромба равна 10см, а один из его углов равен 30° Найдите радиус окружности вписанной в ромб

Answer 1

Проведем высоту. Известно, что катет лежащий против угла 30 градусов в два раза меньше гипотенузы. Значит высота ромба равна h=5 см. Радиус вписанной окружности в ромб равен r=h/2, r=5/2=2,5 см.

Answer 2

Problem Analysis

We are given that one side of a rhombus is equal to 10 cm and one of its angles is 30°. We need to find the radius of the circle inscribed in the rhombus.

Solution

To find the radius of the circle inscribed in the rhombus, we can use the formula:

Radius of the inscribed circle = (Side length of the rhombus) / 2 * sin(Angle of the rhombus)

Substituting the given values, we have:

Radius of the inscribed circle = (10 cm) / 2 * sin(30°)

Let's calculate the value of the radius using this formula.

Calculation

Using the formula, we can calculate the radius of the inscribed circle as follows:

Radius of the inscribed circle = (10 cm) / 2 * sin(30°)

Calculating the value:

Radius of the inscribed circle = (10 cm) / 2 * 0.5 Simplifying the expression:

Radius of the inscribed circle = 5 cm

Answer

The radius of the circle inscribed in the rhombus is 5 cm.

Please let me know if there is anything else I can help you with.