In triangle ABC AB = 12cm, BC = 18cm, angle B = 70 degrees, and in triangle MNC MH = 6cm

In triangle ABC AB = 12cm, BC = 18cm, angle B = 70 degrees, and in triangle MNC MH = 6cm, HK = 9cm, angle = 70 degrees. Find the side AC and the angle C of the triangle ABC, if MK = 7cm, angle K = 60 degrees.

Let us prove that triangle ABC is similar to triangle MNK.

Angle CBA = KHM = 70. Let’s find the ratio of the sides adjacent to these angles.

BC / HK = 18/9 = 2.

AB / MH = 12/6 = 2.

Since the sides are proportional, and the angle between them is the same, the triangles ABC and MNK are similar in the second feature of the similarity of triangles, two proportional sides and the angle between them.

Then the angle ACB = MKN = 60, side AC = 2 * KM = 2 * 7 = 14 cm.

Answer: The AC side is 14 cm, the C angle is 60.