To determine The area of cross section of the tunnel. Explanation Formula used: The area of any sector of a circle in terms of the radius r and central angle θ (in radians) is given by A = 1 2 θ r 2 . Area of a triangle of base b and height h is given by A = 1 2 b h . Procedure used: “Procedure for converting angle measurements: To convert an angle measured in degrees to the same angle measured in radians, multiply the number of degrees by π rad 180 ° .” Theorem used: Pythagorean Theorem: In a right angle triangle, ( Hypotenuse ) 2 = ( Base ) 2 + ( Height ) 2 . Calculation: It is given that cross section of a tunnel is the major segment of a circle of radius 12.0 ft wide and the base of the tunnel is 20.0 ft wide. The given information can be diagrammatically represented as shown below: From Figure 1, it can be seen that the vertices of right triangle is labelled with A, B, and C and height of the triangle Δ ABC is h . Using Pythagorean theorem, obtain the height of the Δ ABC as follows: ( Hypotenuse ) 2 = ( Base ) 2 + ( Height ) 2 12 2 = 10 2 + h 2 h = 12 2 − 10 2 h = 44 h = 6.63 ft Hence, h = 6.63 ft . From Δ ABC in Figure 1, it can be observed that sin θ = 10 12 . Thus, θ = sin − 1 ( 10 12 ) = 56.4 ° Therefore, θ = 56.4 ° . If θ = 56.4 ° , then the value of 2 θ is obtained as follows: 2 θ = 2 ( 56.4 ° ) = 112.9 ° Thus, 2 θ = 112.9 ° . Convert the angle 2 θ = 112.9 ° into radian measure as shown below: 2 θ = 112.9 ° = 112.9 ° ( π rad 180 ° ) = 1.97 rad Thus, 2 θ = 1.97 rad . Substitute r = 12 and 2 θ = 1.97 rad in A = 1 2 r 2 ( θ − sin θ ) and obtain the area of the sector A sector as follows: A sector = 1 2 θ r 2 = 1 2 ( 1.97 ) ( 12 ) 2 = 141.86 ft 2 Thus, area of the sector A sector is 141.86 ft 2 . Substitute r = 12 and 2 θ = 1

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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Chapter 8, Problem 80RE

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Chapter 8, Problem 79RE

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Chapter 8 Solutions

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

Ch. 8.1 - Determine the sign of the given functions: sin...Ch. 8.1 - In Example 4, if 90° is added to each angle, what...Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - In Exercises 3–16, determine the sign of the given...Ch. 8.1 - Prob. 7E Ch. 8.1 - In Exercises 3–16, determine the sign of the given...Ch. 8.1 - Prob. 9E

Ch. 8.1 - Prob. 10E Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - In Exercises 3–16, determine the sign of the given...Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - In Exercises 17–24, find the trigonometric...Ch. 8.1 - Prob. 21E Ch. 8.1 - In Exercises 17–24, find the trigonometric...Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - In Exercises 25–30, for the given values,...Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - In Exercises 31–40, determine the quadrant in...Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - In Exercises 31–40, determine the quadrant in...Ch. 8.1 - Prob. 39E Ch. 8.1 - Prob. 40E Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.2 - Express each function in terms of the reference...Ch. 8.2 - Prob. 2PE Ch. 8.2 - Express each function in terms of the reference...Ch. 8.2 - Practice Exercise 4. If cos θ = 0.5736, find θ for...Ch. 8.2 - Prob. 5PE Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - In Exercises 3–8, express the given trigonometric...Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Prob. 11E Ch. 8.2 - In Exercises 9–42, the given angles are...Ch. 8.2 - Prob. 13E Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - In Exercises 17–24, find the values of the given...Ch. 8.2 - Prob. 19E Ch. 8.2 - In Exercises 17–24, find the values of the given...Ch. 8.2 - In Exercises 17–24, find the values of the given...Ch. 8.2 - In Exercises 17–24, find the values of the given...Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - Prob. 30E Ch. 8.2 - Prob. 31E Ch. 8.2 - In Exercises 25‒38, find θ for 0° ≤ θ < 360°. 32....Ch. 8.2 - Prob. 33E Ch. 8.2 - Prob. 34E Ch. 8.2 - Prob. 35E Ch. 8.2 - Prob. 36E Ch. 8.2 - Prob. 37E Ch. 8.2 - Prob. 38E Ch. 8.2 - Prob. 39E Ch. 8.2 - In Exercises 39–42, find the exact value of each...Ch. 8.2 - Prob. 41E Ch. 8.2 - Prob. 42E Ch. 8.2 - Prob. 43E Ch. 8.2 - Prob. 44E Ch. 8.2 - Prob. 45E Ch. 8.2 - Prob. 46E Ch. 8.2 - Prob. 47E Ch. 8.2 - Prob. 48E Ch. 8.2 - Prob. 49E Ch. 8.2 - Prob. 50E Ch. 8.2 - Prob. 51E Ch. 8.2 - Prob. 52E Ch. 8.2 - Prob. 53E Ch. 8.2 - Prob. 54E Ch. 8.2 - Prob. 55E Ch. 8.2 - Prob. 56E Ch. 8.2 - Prob. 57E Ch. 8.2 - Prob. 58E Ch. 8.2 - Prob. 59E Ch. 8.2 - Prob. 60E Ch. 8.3 - Prob. 1PE Ch. 8.3 - Prob. 2PE Ch. 8.3 - Prob. 3PE Ch. 8.3 - Prob. 4PE Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Prob. 4E Ch. 8.3 - Prob. 5E Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Prob. 17E Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - In Exercises 19–26, express the given angles in...Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - Prob. 31E Ch. 8.3 - Prob. 32E Ch. 8.3 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E Ch. 8.3 - Prob. 39E Ch. 8.3 - Prob. 40E Ch. 8.3 - In Exercises 35–42, evaluate the given...Ch. 8.3 - In Exercises 35–42, evaluate the given...Ch. 8.3 - In Exercises 43–50, evaluate the given...Ch. 8.3 - Prob. 44E Ch. 8.3 - Prob. 45E Ch. 8.3 - Prob. 46E Ch. 8.3 - Prob. 47E Ch. 8.3 - Prob. 48E Ch. 8.3 - In Exercises 43–50, evaluate the given...Ch. 8.3 - Prob. 50E Ch. 8.3 - Prob. 51E Ch. 8.3 - Prob. 52E Ch. 8.3 - Prob. 53E Ch. 8.3 - Prob. 54E Ch. 8.3 - Prob. 55E Ch. 8.3 - Prob. 56E Ch. 8.3 - In Exercises 51–58, find θ to four significant...Ch. 8.3 - In Exercises 51–58, find θ to four significant...Ch. 8.3 - 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Prob. 15RE Ch. 8 - Prob. 16RE Ch. 8 - Prob. 17RE Ch. 8 - Prob. 18RE Ch. 8 - In Exercises 19–26, the given numbers represent...Ch. 8 - Prob. 20RE Ch. 8 - Prob. 21RE Ch. 8 - Prob. 22RE Ch. 8 - Prob. 23RE Ch. 8 - Prob. 24RE Ch. 8 - Prob. 25RE Ch. 8 - Prob. 26RE Ch. 8 - Prob. 27RE Ch. 8 - Prob. 28RE Ch. 8 - Prob. 29RE Ch. 8 - Prob. 30RE Ch. 8 - Prob. 31RE Ch. 8 - Prob. 32RE Ch. 8 - In Exercises 33–36, express the given angles in...Ch. 8 - Prob. 34RE Ch. 8 - Prob. 35RE Ch. 8 - Prob. 36RE Ch. 8 - Prob. 37RE Ch. 8 - In Exercises 37–56, determine the values of the...Ch. 8 - Prob. 39RE Ch. 8 - In Exercises 37–56, determine the values of the...Ch. 8 - Prob. 41RE Ch. 8 - Prob. 42RE Ch. 8 - Prob. 43RE Ch. 8 - Prob. 44RE Ch. 8 - Prob. 45RE Ch. 8 - Prob. 46RE Ch. 8 - Prob. 47RE Ch. 8 - Prob. 48RE Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - Prob. 51RE Ch. 8 - Prob. 52RE Ch. 8 - Prob. 53RE Ch. 8 - In Exercises 37–56, determine the values of the...Ch. 8 - Prob. 55RE Ch. 8 - Prob. 56RE Ch. 8 - Prob. 57RE Ch. 8 - Prob. 58RE Ch. 8 - Prob. 59RE Ch. 8 - Prob. 60RE Ch. 8 - Prob. 61RE Ch. 8 - Prob. 62RE Ch. 8 - Prob. 63RE Ch. 8 - Prob. 64RE Ch. 8 - Prob. 65RE Ch. 8 - Prob. 66RE Ch. 8 - Prob. 67RE Ch. 8 - Prob. 68RE Ch. 8 - Prob. 69RE Ch. 8 - Prob. 70RE Ch. 8 - Prob. 71RE Ch. 8 - Prob. 72RE Ch. 8 - Prob. 73RE Ch. 8 - Prob. 74RE Ch. 8 - Prob. 75RE Ch. 8 - Prob. 76RE Ch. 8 - In Exercises 77–103, solve the given...Ch. 8 - Prob. 78RE Ch. 8 - Prob. 79RE Ch. 8 - In Exercises 77–103, solve the given problems. 80....Ch. 8 - Prob. 81RE Ch. 8 - Prob. 83RE Ch. 8 - Prob. 84RE Ch. 8 - Prob. 85RE Ch. 8 - Prob. 87RE Ch. 8 - Prob. 88RE Ch. 8 - Prob. 89RE Ch. 8 - Prob. 90RE Ch. 8 - Prob. 92RE Ch. 8 - Prob. 93RE Ch. 8 - Prob. 94RE Ch. 8 - Prob. 95RE Ch. 8 - Prob. 96RE Ch. 8 - Prob. 97RE Ch. 8 - Prob. 98RE Ch. 8 - Prob. 99RE Ch. 8 - The Trans-Alaska Pipeline was assembled in...Ch. 8 - Prob. 101RE Ch. 8 - Prob. 102RE Ch. 8 - Prob. 103RE Ch. 8 - Prob. 1PT Ch. 8 - Prob. 2PT Ch. 8 - Prob. 3PT Ch. 8 - Prob. 4PT Ch. 8 - Prob. 5PT Ch. 8 - 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