SINE PROBLEMS

BASIC

Concept: In a right triangle, the sine of the angle is what we call the ratio of the side opposite the angle and the hypotenuse.

Steps For Solving Sine Problems

Step 1 | Determine the length of the side which is opposite the angle in question.
Step 2 | Determine the length of the hypotenuse.
Step 3 | Set up a ratio using the length of the side opposite 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 sine of the angle in question.

Example 1 Find the sine of the following angle:

Step 1 | Determine the length of the side which is opposite the angle in question. | 20.706
Step 2 | Determine the length of the hypotenuse. | 80
Step 3 | Set up a ratio using the length of the side opposite the angle as the numerator, and the hypotenuse as the denominator. | 20.706 80
Step 4 | Divide the numerator by the denominator. |
Step 5 | The quotient is the sine of the angle in question. | 0.258
Program Note | In this program, you are often asked to round your answer, in this case to the nearest hundredth. | 0.26

Example 2 You are standing several meters away from the base of a flagpole. The flagpole is 60 meters tall. There are 120 meters between you and the top of the flagpole. What is the value of sine from the point at which you are standing?

NOTE: | Since you have been asked to find the value of sine 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 flagpole and the ground is 90 degrees. The flagpole will form one side of the right triangle, and the ground will form the other side. The line from you to the top of the flagpole will form the hypotenuse. |
Step 1 | Determine the length of the side which is opposite the angle in question. | 60
Step 2 | Determine the length of the hypotenuse. | 120
Step 3 | Set up a ratio using the length of the side opposite the angle as the numerator, and the hypotenuse as the denominator. | 60 . 120
Step 4 | Divide the numerator by the denominator. |
Step 5 | The quotient is the sine of the angle in question. | 0.5
Program Note: | In this program, you are often asked to round your answer, in this case to the nearest hundredth. | 0.5