In triangle ABC. AC = 7cm AB = 5cm BC = 8cm. Find the cosine of the angle A.

Given:
triangle ABC,
AC = 7 centimeters,
AB = 5 centimeters,
BC = 8 centimeters.
Find cos A -?
Decision:
Consider a triangle ABC. By the cosine theorem (the square of a side is equal to the sum of the squares of the other two sides without doubled the product of these sides by the angle between them):
BC ^ 2 = AB ^ 2 + AC ^ 2 – 2 * AB * AC * cos A;
8 ^ 2 = 5 ^ 2 + 7 ^ 2 – 2 * 5 * 7 * cos A;
64 = 25 + 49 – 70 * cos A;
64 = 74 – 70 * cos A;
70 * cos A = 74 – 64;
70 * cos A = 10;
cos A = 10: 70;
cos A = 10/70;
cos A = 1/7.
Answer: cos A = 1/7.