In triangle ABC, angle C is 90 °, BC = 15. The radius of the circumscribed circle of this triangle is 8.5. Find the AC.

univerkov | August 24, 2021 | education

Since a right-angled triangle is inscribed in a circle, the hypotenuse of a right-angled triangle coincides with the diameter of the circle, then the hypotenuse AB = 2 * R = 2 * 8.5 = 17 cm.

By the Pythagorean theorem, we determine the length of the leg AC.

AC ^ 2 = AB ^ 2 – BC ^ 2 = 17 ^ 2 – 15 ^ 2 = 289 – 225 = 64.

AC = 8 cm.

Answer: The length of the speaker side is 8 cm.

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