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EXAMPLE 3

The correct answer is C. ANSWER. 6. 6. adj. 56.9°. θ. cos – 1. =. cos θ. =. =. 11. 11. hyp. EXAMPLE 3. Standardized Test Practice. SOLUTION.

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EXAMPLE 3

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  1. The correct answer is C. ANSWER 6 6 adj 56.9° θ cos – 1 = cosθ = = 11 11 hyp EXAMPLE 3 Standardized Test Practice SOLUTION In the right triangle, you are given the lengths of the side adjacent to θ and the hypotenuse, so use the inverse cosine function to solve for θ.

  2. Monster Trucks EXAMPLE 4 Write and solve a trigonometric equation A monster truck drives off a ramp in order to jump onto a row of cars. The ramp has a height of 8 feet and a horizontal length of 20 feet. What is the angle θ of the ramp?

  3. Draw: a triangle that represents the ramp. 8 opp tanθ = = 20 adj EXAMPLE 4 Write and solve a trigonometric equation SOLUTION STEP 1 Write: a trigonometric equation that involves the ratio of the ramp’s height and horizontal length. STEP 2

  4. ANSWER The angle of the ramp is about 22°. 8 21.8° θ tan–1 = 20 EXAMPLE 4 Write and solve a trigonometric equation STEP 3 Use: a calculator to find the measure of θ.

  5. 11. 4 4 9 9 θ = cosθ adj 63.6° cos–1 = = hyp for Examples 3 and 4 GUIDED PRACTICE Find the measure of the angle θ. SOLUTION In the right triangle, you are given the lengths of the side adjacent to θand the hypotenuse. So, use the inverse cosine function to solve for θ.

  6. 12. 10 10 8 8 θ tan–1 = tanθ = opp 51.3° = adj for Examples 3 and 4 GUIDED PRACTICE Find the measure of the angle θ. SOLUTION In the right triangle, you are given the lengths of the side opposite to θand the side adjacent. So, use the inverse tan function to solve for θ.

  7. 13. 5 5 12 12 θ sin–1 = sinθ = opp 24.6° = hyp for Examples 3 and 4 GUIDED PRACTICE Find the measure of the angle θ. SOLUTION In the right triangle, you are given the lengths of the side opposite to θand the hypotenuse. So, use the inverse sin function to solve for θ.

  8. 14. WHAT IF? In Example 4, suppose a monster truck drives 26feet on a ramp before jumping onto a row of cars. If the ramp is 10 feet high, what is the angle θof the ramp? opp 10 = = adj 26 tanθ for Examples 3 and 4 GUIDED PRACTICE SOLUTION Draw: a triangle that represents the ramp. STEP 1 Write: a trigonometric equation that involves the ratio of the ramp’s height and horizontal length. STEP 2

  9. 10 22.6° θ tan–1 = 26 ANSWER The angle of the ramp is about 22.6°. for Examples 3 and 4 GUIDED PRACTICE STEP 3 Use: a calculator to find the measure of θ.

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