TANGENT PROBLEMS

INTERMEDIATE

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

Steps For Solving Tangent Problems

Step 1 | Determine the length of the side which is opposite the angle in question.
Step 2 | Determine the length of the side which is adjacent to the angle in question (and which is not the hypotenuse).
Step 3 | Set up a ratio using the length of the side opposite the angle as the numerator, and the length of the side adjacent to the angle as the denominator.
Step 4 | Divide the numerator by the denominator.
Step 5 | The quotient is the tangent 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. | 54.94
Step 2 | Determine the length of the side which is adjacent to the angle in question (and which is not the hypotenuse). | 117.82
Step 3 | Set up a ratio using the length of the side opposite the angle as the numerator, and the length of the side adjacent to the angle as the denominator. | 54.94 117.82
Step 4 | Divide the numerator by the denominator. |
Step 5 | The quotient is the tangent of the angle in question. | 0.466
| To find the measure of the angle when you have the tangent of the angle, enter the tangent of the angle on your calculator, and then press the “shift” key followed by the “Tan” key, or on other calculators, it would be the “Inv” key followed by the “Atn” key. | 25°

Example 2 What is Tan 65°?

| To find the tangent of the angle when you have the measure of the angle, enter the measure of the angle on your calculator, followed by the “tan” key. | 2.1445

Example 3 What is the angle A of the following equation? Tan A = 0.364

| To find the measure of the angle when you have the tangent of the angle, enter the tangent of the angle on your calculator, and then press the “shift” key followed by the “Tan” key, or on other calculators, it would be the “Inv” key followed by the “Atn” key. | 20 degrees