In triangle ABC, angle C is 90 degrees BC = 12 AC = 16 find cosA

Given:

right-angled triangle ABC;

angle C = 90;

BC = 12;

AC = 16;

Find: cosA -?

Solution:

1. Consider a right-angled triangle ABC.

By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

AC ^ 2 + BC ^ 2 = AB ^ 2;

16 ^ 2 + 12 ^ 2 = AB ^ 2;

256 + 144 = AB ^ 2;

400 = AB ^ 2;

AB = 20.

2. The cosine of an angle in a right-angled triangle is equal to the ratio of the adjacent leg to the hypotenuse. Consequently:

cos A = AC / AB;

cos A = 16/20;

cos A = 4/5.

Answer: cos A = 4/5.