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.

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Right Triangle Trigonometry

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Presentation transcript:

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. cos θ = adj hyp = 6 11 cos – 1 θ = ° The correct answer is C.ANSWER

EXAMPLE 4 Write and solve a trigonometric equation Monster Trucks 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?

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

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

GUIDED PRACTICE for Examples 3 and 4 Find the measure of the angle θ. 11. 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. cos θ = adj hyp = 4 9 = 63.6° θcos –1 4 9

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

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

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

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