Explanation Given: The shaded rectangular area is of length 18 feet and width 8 feet. The stalls for diagonal parking are arranged at an angle θ = 25 ° . The given Figure is redrawn as follows. Formula used: Trigonometric ratios: sin θ = Opposite Hypotenuse ; csc θ = Hypotenuse Opposite cos θ = Adjacent Hypotenuse ; sec θ = Hypotenuse Adjacent tan θ = Opposite Adjacent ; cot θ = Adjacent Opposite Calculation: From the given Figure it can be observed that the sides of same length have been marked with a dash line. One among the four stalls for diagonal parking is as shown below in Figure 1. From Figure 1 it can be observed that there are 3 right triangles Δ q v r , Δ r u s and Δ s p t respectively . Use the result that angles on a straight line is equal to 180 ° and obtain the value of θ 1 as follows. 25 ° + 90 ° + θ 1 = 180 ° 115 ° + θ 1 = 180 ° θ 1 = 65 ° From the right triangle Δ r u s in Figure 1, use the trigonometric ratios of sin θ and cos θ in order to obtain the adjacent and opposite sides to the angle θ = 25 ° . sin 25 ° = s u s r s u = s r ⋅ sin 25 ° s u = 18 × sin 25 ° s u = 7.6 Compute the side ru as follows. cos 25 ° = A d j a c e n t H y p o t e n u s e r u = s r ⋅ cos 25 ° r u = 18 × cos 25 ° r u = 16.3 From right triangle Δ q v r in Figure 1, use the trigonometric ratios sin θ and cos θ in order to obtain the adjacent and opposite sides to θ 1 = 65 ° . sin 65 ° = q v q r q v = q r ⋅ sin 65 ° q v = 8 × sin 65 ° q v = 7

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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Chapter 8.1, Problem 55E

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To find: The dimensions x and y approximated to the nearest tenth of a foot.

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Chapter 8.1, Problem 54E

Chapter 8.1, Problem 56E

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Chapter 8 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

Ch. 8.1 - Find the degree measure of 1 rad.Ch. 8.1 - Without using a calculator, find: (A)cot 45 (B)cos...Ch. 8.1 - Solve the right triangle in Figure 14. Round side...Ch. 8.1 - Solve the right triangle in Figure 16. Round...Ch. 8.1 - Repeat Example 5 assuming that the man is standing...Ch. 8.1 - Prob. 1ED Ch. 8.1 - Prob. 1E Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...

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The dimensions x and y approximated to the nearest tenth of a foot.

Solution Summary: The author calculates the dimensions x and y approximated to the nearest tenth of a foot. The stalls for diagonal parking are arranged at an angle theta =25°

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To find: The dimensions x and y approximated to the nearest tenth of a foot.

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Chapter 8 Solutions