COSINE PROBLEMS

INTERMEDIATE

Concept: In a right triangle, the cosine of the angle is what we call the ratio of the side adjacent to the angle and the hypotenuse.

Steps For Solving Cosine Problems

Step 1 | Determine the length of the side which is adjacent to the angle in question (and which is not the hypotenuse).
Step 2 | Determine the length of the hypotenuse.
Step 3 | Set up a ratio using the length of the side adjacent to the angle as the numerator and the hypotenuse as the denominator.
Step 4 | Divide the numerator by the denominator.
Step 5 | The quotient is the cosine of the angle in question.

Example 1 Solve for the unknown variable:

Step 1 | Determine the length of the side which is adjacent to the angle in question (and which is not the hypotenuse). | 38.567
Step 2 | Determine the length of the hypotenuse. | 60
Step 3 | Set up a ratio using the length of the side adjacent to the angle as the numerator, and the hypotenuse as the denominator. | 38.567 60
Step 4 | Divide the numerator by the denominator. |
Step 5 | The quotient is the cosine of the angle in question. | 0.642
| To find the measure of the angle when you have the cosine of the angle, enter the cosine of the angle on your calculator, and then press the “shift” key followed by the “cos” key, or on other calculators, it would be the “Inv” key followed by the “Acs” key. | 52

Example 2 What is Cos 55°?

| To find the cosine of the angle when you have the measure of the angle, enter the measure of the angle on your calculator, followed by the “cos” key. | 0.574

Example 3 What is the angle A of the following equation? Cos A = 0.985

| To find the measure of the angle when you have the cosine of the angle, enter the cosine of the angle on your calculator, and then press the “shift” key followed by the “cos” key, or on other calculators, it would be the “Inv” key followed by the “Acs” key. | 10 degrees