In triangle ABC, angle C is 90 degrees, BC = root 135. The radius of the circle circumscribed

In triangle ABC, angle C is 90 degrees, BC = root 135. The radius of the circle circumscribed about this triangle is 8, find AC.

Since the circle is circumscribed about a right-angled triangle, the degree measure of the arc AB is equal to two values of the angle ACB, then the arc AB = 2 * 90 = 180, and therefore AB is the diameter of the circumscribed circle.

AB = 2 * R = 2 * 8 = 16 cm.

Then, by the Pythagorean theorem, we determine the length of the leg AC.

AC ^ 2 = AB ^ 2 – BC ^ 2 = 16 ^ 2 – (√135) ^ 2 = 256 – 135 = 121.

AC = 11 cm.

Answer: The length of the speaker side is 11 cm.