In the triangle ABC, the angle C = 90 degrees, AC = 4√91, AB = 40 find cosB.

Find cos b in triangle abc.

It is known:

Angle c = 90 °;
ac = 4√91;
ab = 40.
Solution.

1) Find leg bc if the hypotenuse and leg of the triangle are known. We apply the Pythagorean theorem.

bc = √ (ab ^ 2 – ac ^ 2) = √ (40 ^ 2 – (4√91) ^ 2) = √ (1600 – 16 * 91) = √ (1600 – 1456) = √144 = 12;

2) cos b = bc / ab (the ratio of the adjacent leg to the hypotenuse);

Since the leg bc = 12 and the hypotenuse ab = 40 are known to us, we will find cos b substituting the known values.

cos b = 12/40 = (4 * 3) / (4 * 10) = 3/10;

Hence, cos b = 3/10.