8.1.2 Trigonometric Ratios (continued) Example 5 Problem-Solving Application
The length of one leg of a right triangle is determined using a trigonometric ratio in this application example. The triangle represents a ramp and the angle with the ground is given as 4.1 ° , while the length of the rise is given as 1.6 ft. The unknown length, x , is the distance along the ground of the ramp, which is the length of the side adjacent to the known angle. The side with known length is opposite the known angle. Thus, the tangent is the appropriate ratio to use. Write the trigonometric ratio for the tangent of 4.1 ° and substitute the given values and the unknown, x . Isolate the unknown, and use a calculator to find the value of tan 4.1 ° and solve for x . The solution yields x ≈ 22.32 ft.
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