Question

Сторона і протележний їй кут трикутника відповідно дорівнюють 10см і 50°. Знайти радіус кола, описаного навколо трикутника

Answer 1

Problem Analysis

We are given a triangle with one side measuring 10 cm and an opposite angle measuring 50°. We need to find the radius of the circle circumscribed around the triangle.

Solution

To find the radius of the circle circumscribed around a triangle, we can use the formula known as the circumradius formula. The circumradius (R) of a triangle is given by the formula:

R = (a / (2 * sin(A)))

Where: - R is the radius of the circumcircle - a is the length of one side of the triangle - A is the measure of the opposite angle

In this case, we are given that one side of the triangle measures 10 cm and the opposite angle measures 50°. Let's substitute these values into the formula to find the radius.

R = (10 / (2 * sin(50°)))

Now, we need to calculate the value of sin(50°). Using a calculator or trigonometric table, we find that sin(50°) is approximately 0.766.

R = (10 / (2 * 0.766))

Simplifying the expression further:

R = (10 / 1.532) R ≈ 6.527 cm

Therefore, the radius of the circle circumscribed around the triangle is approximately 6.527 cm.

Answer

The radius of the circle circumscribed around the triangle is approximately 6.527 cm.