COSINE PROBLEMS

BASIC

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 Sine 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 Find the Cosine of the following angle:

Step 1 | Determine the length of the side which is adjacent to the angle in question (and which is not the hypotenuse). | 33.646
Step 2 | Determine the length of the hypotenuse. | 130
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. | 33.646 130
Step 4 | Divide the numerator by the denominator. |
Step 5 | The quotient is the cosine of the angle in question. | 0.258
Program Note | In this program it is often necessary to round the answer, in this case to the nearest hundredth. | 0.26

Example 2 You are standing 41.042 centimeters from the base of a flimsy tree. There are 120 centimeters between you and the top of the flimsy tree. What is the value of cosine from the point at which you are standing?

NOTE: | Since you have been asked to find the value of cosine in this word problem, you know that you are dealing with a triangle. Set up the triangle using the information given in the word problem. |
| The angle formed by the flimsy tree and the ground is 90 degrees. The flimsy tree will form one side of the right triangle, and the line on the ground between you and the flimsy tree will form the other side. The line from you to the top of the flimsy tree will form the hypotenuse. |
Step 1 | Determine the length of the side which is adjacent to the angle in question (and which is not the hypotenuse). | 41.042
Step 2 | Determine the length of the hypotenuse. | 120
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. | 41.042 . 120
Step 4 | Divide the numerator by the denominator. |
Step 5 | The quotient is the cosine of the angle in question. | 0.342
Program Note: | In this program, you are often asked to round your answer, in this case to the nearest hundredth. | 0.34