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 of θ = 40 ° . The given figure can be 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 in Figure 1. From Figure 1 it can be observed that there are 3 right angled triangles Δ q v r , Δ r u s and Δ s p t . The value of θ 1 is obtained as, 40 ° + 90 ° + θ 1 = 180 ° 130 ° + θ 1 = 180 ° θ 1 = 50 ° Consider Δ r u s in Figure 1, use the trigonometric ratios sin θ and cos θ in order to obtain the adjacent and opposite sides to θ = 40 ° . sin 40 ° = s u s r s u = ( s r ) ⋅ sin 40 ° s u = 18 × sin 40 ° s u = 11.6 Compute the side ur as follows. cos 40 ° = u r s r u r = ( s r ) ⋅ cos 40 ° u r = 18 × cos 40 ° u r = 13.8 Consider 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 = 50 ° . sin 50 ° = q v q r q v = ( q r ) ⋅ sin 50 ° q v = 8 × sin 50 ° q v = 6

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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Chapter 8.1, Problem 56E

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To find: The dimensions of x and y.

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Chapter 8.1, Problem 55E

Chapter 8.1, Problem 57E

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Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

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The dimensions of x and y .

Solution Summary: The author explains how the dimensions of x and y are 48.9 and 18.9 ft, respectively. The stalls for diagonal parking are arranged at an angle of theta =40°

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To find: The dimensions of x and y.

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