In a triangle ABC AC = 7.5 BC = 4, angle C = 90 degrees. Find the radius of the inscribed circle.

Since the triangle ABC is rectangular, we find the hypotenuse: AB ^ 2 = AC ^ 2 + BC ^ 2 => AB ^ 2 = 16 + 56.25 <=> AB = 8.5. Let’s find the area of the triangle ABC: S = AC * BC / 2 = 4 * 7.5 / 2 = 15 sq. units There is another formula for the area of a triangle: S = p * r, where p is a semi-perimeter, r is the radius of the inscribed circle. So, 15 = r * (AC + BC + AB) / 2 15 = r * (4 + 8.5 + 7.5) / 2 <=> 15 = 10 * r <=> r = 1.5.
Answer: r = 1.5