Triangle ABC is rectangular. angle C = 90 degrees, angle B = 27 degrees, CD – height, CK – bisector

Triangle ABC is rectangular. angle C = 90 degrees, angle B = 27 degrees, CD – height, CK – bisector of angle ACB, find angle DCK.

Consider a triangle BCD:

Angle B is equal to 27 ° (by condition), angle D is equal to 90 ° (since CD is the height), which means that DCB is 180 ° – (90 ° + 27 °) = 180 ° – 117 ° = 63 °.

The angle ВСК is equal to 45 °, since СК is the bisector of the right angle C.

This means that the angle DCК = DCВ – ВСК = 63 ° – 45 ° = 18 °.

Answer: the DCK angle is 18 °.