# In a right-angled triangle from the vertex of an angle equal to 60 degrees, a bisector is drawn

January 15, 2021 | education

| **In a right-angled triangle from the vertex of an angle equal to 60 degrees, a bisector is drawn, the length of which is 18 cm. Find the length of the leg, which lies opposite the given angle.**

Since the segment AM is the bisector of the angle CAB, the angle CAM = CAB / 2 = 60/2 = 30.

In a right-angled AСМ triangle, the CM leg is located opposite an angle of 30, then CM = AM / 2 = 18/2 = 9 cm.

Angle BAM = CAB / 2 = 60/2 = 30, angle ABM = (90 – BAC) = (90 – 60) = 30.

Then in triangle ABM the angles at the base of AB are equal to 30, then ABM is an isosceles triangle, then BM = AM = 18 cm.

Leg length BC = CM + BM = 9 + 18 = 27 cm.

Answer: The length of the leg is 27 cm.

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