In triangle CDE CM-bisector, angle DCE = 60 degrees, ME = 3√2. Find CM if CED = 45 degrees.

univerkov | September 5, 2021 | education

Since, by condition, CM is a bisector, then the angle ECM = DCM = DCE / 2 = 60/2 = 30.

We use the theorem of sines for triangles to solve the problem. The ratio of each side of the triangle to the sine of the opposite angle is equal.

CM / SinЕ = ME / SinЕМС.

CM / Sin450 = 3 * √2 / Sin300.

3 * √2 * (√2 / 2) = CM * (1/2).

CM = 3 * 2 = 6 cm.

Answer: CM = 6 cm.

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