In a right-angled triangle CDK, the angle C is straight, CM is the height, angle K is 60 degrees

In a right-angled triangle CDK, the angle C is straight, CM is the height, angle K is 60 degrees, CD is the root of 2. Find CM.

Determine the angles of the CDM triangle.

Let’s define the angle СDК of the triangle СDК. Angle СDК = 180 – 90 – 60 = 30.

Since CM is the height of the triangle, then the angle CMD = 90, then the angle DCM = 180 – 90 – 30 = 60.

In a right-angled triangle CDM, the CM leg lies opposite an angle of 30, then CM = CD / 2 = √2 / 2 cm.

Answer: The length of the CM height is √2 / 2 cm.