SINE PROBLEMS

INTERMEDIATE

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 Solve for the unknown variable:

Step 1 | Determine the length of the side which is opposite the angle in question. | 50.714
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. | 50.714 120
Step 4 | Divide the numerator by the denominator. |
Step 5 | The quotient is the sine of the angle in question. | 0.4226
| To find the measure of the angle when you have the sine of the angle, enter the sine of the angle on your calculator, and then press the “shift” key followed by the “sin” key, or on other calculators, it would be the “Inv” key followed by the “Asn” key. | 25 degrees

Example 2 What is Sin 45°?

| To find the sine of the angle when you have the measure of the angle, enter the measure of the angle on your calculator, followed by the “sin” key. | 0.7071

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

| To find the measure of the angle when you have the sine of the angle, enter the sine of the angle on your calculator, and then press the “shift” key followed by the “sin” key, or on other calculators, it would be the “Inv” key followed by the “Asn” key. | 80 degrees