In a triangle ABC = 21, the angle C is 90, the radius of the circumscribed circle of this triangle is 14.5. find AC.

In triangle ABC it is known:

Angle C = 90 °;
BC = 21;
A circle is described;
R = 14.5;
Find AC.

Since the circle is described around a right-angled triangle, then the radius of the circle is half the hypotenuse.

R = 1/2 * AB;

Hence, AB = 2 * R = 2 * 14.5 = 29.

Since the hypotenuse and one leg are known, we will find the second leg of the right triangle.

AC = √ (AB ^ 2 – BC ^ 2) = √ (29 ^ 2 – 21 ^ 2) = √ ((29 – 21) * (29 + 21)) = √ (8 * 50) = √400 = √ 20 ^ 2 = 20;

As a result, we got that the leg of a right-angled triangle is equal to AC = 20.