In triangle ABC it is known that AC = 8, BC = 15, angle C is 90 °. Find the radius of the circle circumscribed about this triangle?

The radius of a circle circumscribed about a right-angled triangle is found by the formula:
R = c / 2,
where c is the hypotenuse.
In △ ABC, the hypotenuse is side AB, since it lies opposite ∠C, which is 90 °. Then the sides AC = 8 and BC = 15 are legs.
By the Pythagorean theorem, we find the length of the hypotenuse AB:
AB = √ (AC² + BC²);
AB = √ (8² + 15²);
AB = √ (64 + 225);
AB = √289;
AB = 17.
Thus, the radius of a circle circumscribed about a given rectangular △ ABC is equal to:
R = AB / 2 = 17/2 = 8.5.
Answer: R = 8.5.