In a triangle ABC AB = 6cm, BC = 8cm, AC = 4cm. Find the cosine of the angle C.

In the ABC triangle it is known:

AB = 6 cm;

BC = 8 cm;

AC = 4 cm.

Find cos C.

In order to find cos C we apply the cosine theorem.

AB ^ 2 = AC ^ 2 + BC ^ 2 – 2 * AC * BC * cos C;

Substitute the known values into the formula and calculate cos C.

6 ^ 2 = 4 ^ 2 + 8 ^ 2 – 2 * 4 * 8 * cos C;

36 = 16 + 64 – 8 * 8 * cos C;

36 = 80 – 64 * cos C;

We leave the unknown values on one side, and transfer the known values to one side. Then we get:

36 – 80 = -64 * cos C;

-44 = -64 * cos C;

44 = 64 * cos C;

cos C = 44/64;

cos C = 11/16.