In the triangle ABC, AB = 12cm, BC = 18cm, angle B = 70 * (degrees), and in the triangle MNK, MN = 6cm, NK = 9cm, angle N = 70 * (degrees). Find: AC and angle-C of triangle ABC, if MK = 7cm, angle-K = 60 * (degrees)
The sides of triangles ABC and MNK are proportional:
AB / MN = BC / NK;
12/6 = 18/9 = 2;
yr (ABC) = yr (MNK);
We use 2 signs of similarity of triangles (if two sides of one triangle are proportional to two sides of another triangle and the angles formed by these sides are equal, then such triangles are similar).
We have: triangle ABC is similar to triangle MNK with a similarity coefficient of 2.
Find the AC side:
AC = MK * 2 = 7 * 2 = 14 cm;
The ACB angle is equal to the MKN angle, that is, it is equal to 60 degrees.
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