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.
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