In a triangle ABC, BC is equal to four and the angle C is equal to 90 degrees, the radius of the circumcircle

In a triangle ABC, BC is equal to four and the angle C is equal to 90 degrees, the radius of the circumcircle of this triangle is 2.5. Find AC.

Since the circle is circumscribed around a right-angled triangle, the center of this circle lies in the middle of the hypotenuse AB of the triangle.

Then AB = 2 * R = 2 * 2.5 = 5 cm.

From the right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the leg AC.

AC ^ 2 = AB ^ 2 – BC ^ 2 = 5 ^ 2 – 4 ^ 2 = 25 – 16 = 9.

AC = 3 cm.

Answer: The length of the speaker side is 3 cm.