Given a right-angled triangle ABC. From the vertex of the right angle C to the hypotenuse

Given a right-angled triangle ABC. From the vertex of the right angle C to the hypotenuse, the bisector CP is dropped. Find the length of the leg AC if AC = 15.

First, let’s draw a triangle ABC, in which the angle C is straight.
Let’s draw the bisector СР, which divides the angle С into СРВ = СРА = 45о.
Since the angle СРВ = 75 °, and the sum of all the angles of the triangle is 180 °, then the angle В = 180 – 75 – 45 = 60 °.
Then, behind the cotangent ratio in a right-angled triangle, we find the second leg CB = 5√3.