Forming a cone 15 cm high makes an angle of 45 degrees with the base plane. Find the radius of the base of the cone.

The top of the cone – S. The center of the circle at the base – O. An arbitrary point lying on the edge of the base circle – H. Angle SOH = 45 degrees. SO is the height that makes an angle of 90 degrees with the base. Hence 180- (45 + 90) = 45 (OSH angle). From this we conclude that the SOH triangle is isosceles and right-angled. Therefore, the height of the cone is equal to the radius of the base. a – the leg of this triangle (radius and height). From the Pythagorean theorem (15 ^ 2 = a ^ 2 + a ^ 2) we express a. a = (15 * √ 2) / 2
Answer: (15 * √2) / 2