In triangle ABC, angle C = 60 °, outside angle at apex B = 120 °. AM is the height to the BC

In triangle ABC, angle C = 60 °, outside angle at apex B = 120 °. AM is the height to the BC side. Find corner A, side AB if MC = 6cm.

The outer angle of a triangle is equal to the sum of its two inner angles that are not adjacent to the outer one.

Angle CBD = ACB + BAC;

120 = 60 + BAC;

BAC = 120 – 60 = 600.

Since the two angles of the triangle are equal to 60, then the ABC triangle is equilateral, and then its height AM is also the median.

Then BM = CM = 6 cm;

BC = BM + CM = 6 + 6 = 12 cm;

AB = BC = BC = 12 cm;

Answer: Side AB = 12 cm, angle BAC = 60.