In a right-angled triangle ABC, angle C is straight, CH is height, CL is bisector, angle LCH = 17 degrees. Find corner B.

The problem has two solutions.

Angle A> B

Since the angle ACB = 90, and the segment CL is the bisector, then the angle BCL = ACL = 90/2 = 45.

Then the angle ACН = ACL – LCH = 45 – 17 = 28.

Since CH is the height of the ABC triangle, then the ACН triangle is rectangular, then the angle СAН = 90 – AСН = 90 – 28 = 62.

Angle ABC = (90 – СAН) = (90 – 62) = 18.

If the angle B> A, then the angle BCH = 45 – 17 = 28, and then the angle BCH = (90 – 28) = 62.

Answer: The angle ABC is 18 or 62.