In triangle ABC, the angle C is 90 °. CH is the height, AC = 5, AH = 3. Find cos B

Given:

ABC – right triangle;

Angle C = 90 degrees;

CH – height;

AC = 5;

AH = 3;

Find cos b.

Decision:

1) From the formula AC ^ 2 = AB * AH we find the hypotenuse AB.

In order to find the hypotenuse AB of the triangle ABC, we use the formula:

AB = AC ^ 2 / AH;

Substitute the known values into the formula and find the hypotenuse AB.

AB = AC ^ 2 / AH = 5 ^ 2/3 = 25/3;

2) From the formula cos b = AC / AB we find cos b.

cos b = 5 / (25/3) = 5/1 * 3/25 = 5/25 * 3 = 1/5 * 3 = 3/5 = 0.6;

As a result, we got that cos b = 0.6.

Answer: cos b = 0.6.