TANGENT PROBLEMS

BASIC

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 Find the tangent of the following angle:

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
Program Note | In this program it is often necessary to round the answer, in this case to the nearest hundredth. | 0.47

Example 2 In a battle, Ironman is thrown across the parking lot, hits a wall, and lands 65 centimeters away from the point from which he was thrown. He had reached a height of 112.583 centimeters when he splattered against the wall. What was the tangent at which he was thrown?

NOTE: | Since you have been asked to find the tangent 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 distance Ironman is thrown forms the side adjacent. The height he is thrown becomes the side opposite. |
Step 1 | Determine the length of the side which is opposite the angle in question. | 112.58365
Step 2 | Determine the length of the side which is adjacent to the angle in question (and which is not the hypotenuse). | 65
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. | 112.583. 65
Step 4 | Divide the numerator by the denominator. |
Step 5 | The quotient is the tangent of the angle in question. | 1.732
Program Note: | In this program, you are often asked to round your answer, in this case to the nearest hundredth. | 1.73