4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

Concept explainers

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.

Videos

Question

Chapter 4.3, Problem 73E

To determine

Find the vertical rise of the inclined plane.

Expert Solution

Answer to Problem 73E

$519.33feet$

Explanation of Solution

Given information:

The Johnstown Inclined Plane in Pennsylvania is one of the longest and steepest hoists in the world. The r $35.4°$ railway cars travel a distance of $896.5$ feet at an angle of approximately $35.4°$ , rising to a height of $1693.5$ feet above sea level.

Find the vertical rise of the inclined plane.

Calculation:

The figure of the Johnstown inclined Plane in Pennsylvania is given below. It is one of the longest and the steepest hoist in the world. The railway cars travel a distance of $896.5$ feet at an angle of $35.4°$ . rising to a height of $1693.5$ feet above the sea level.

We have to find the vertical rise of the inclined plane.

Let $x$ denote the vertical rise of the plane.

Now, from the above figure we can see that the length of the hypotenuse is $896.5$ feet.

The side opposite to the angle $35.4°$ is the vertical rise given by $x$ .

Now , we know that the trigonometric function which involves these two sides, that is the hypotenuse and the opposite to the angle is the sine function given by.

$sinθ=OppositeHypotenuse$

Substituting the values in the above gven formula of sin, we have,

$sin35.4°=x896.5$

$x=896.5×sin35.4°$

$=896.5×0.579$

$=519.33$

Hence, the vertical rise of the plane is $519.33feet$

To determine

Find the elevation of the lower end of the inclined plane.

Expert Solution

Answer to Problem 73E

$1693.5−519.33=1174.17feet$

Explanation of Solution

Given information:

Find the elevation of the lower end of the inclined plane.

Calculation:

The total height of the plane above the sea level is $1693.5$ feet.

From part a we see that the height of the plane is $519.33$ feet.

Hence, the elevation of the lower end of the inclined plane is

$1693.5−519.33=1174.17feet$

To determine

Find the rate at which they rise vertically.

Expert Solution

Answer to Problem 73E

$173.7feet$

Explanation of Solution

Given information:

The cars move up the mountain at a rate of 300 feet per minute. Find the rate at which they rise vertically.

Calculation:

The cars move up the mountain at a rate $300$ feet per minute. We have to find the rate at which that rise vertically. We can assume to speed to be $y$ feet per minute. This can represent the side opposite to the angle $35.4°$ . Also the cars are currently moving up the mountain, which according to the figure above is giving by the hypotenuse.

Hence, the rate at which cars rise vertically is given by the following equation,

$35.4°=y300$

$y=300×sin35.4°$

$=896.5×0.579$

$=173.7$

Hence, the rate at which cars rise vertically is $173.7feet$ .

Chapter 4.3, Problem 72E

Chapter 4.3, Problem 74E

Chapter 4 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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Prob. 97E Ch. 4.7 - Prob. 98E Ch. 4.7 - Prob. 99E Ch. 4.7 - Prob. 100E Ch. 4.7 - Prob. 101E Ch. 4.7 - Prob. 102E Ch. 4.7 - Prob. 103E Ch. 4.7 - Prob. 104E Ch. 4.7 - Prob. 105E Ch. 4.7 - Prob. 106E Ch. 4.7 - Prob. 107E Ch. 4.7 - Prob. 108E Ch. 4.7 - Prob. 109E Ch. 4.7 - Prob. 110E Ch. 4.7 - Prob. 111E Ch. 4.7 - Prob. 112E Ch. 4.7 - Prob. 113E Ch. 4.7 - Prob. 114E Ch. 4.7 - Prob. 115E Ch. 4.7 - Prob. 116E Ch. 4.7 - Prob. 117E Ch. 4.7 - Prob. 118E Ch. 4.7 - Prob. 119E Ch. 4.7 - Prob. 120E Ch. 4.7 - Prob. 121E Ch. 4.7 - Prob. 122E Ch. 4.7 - Prob. 123E Ch. 4.7 - Prob. 124E Ch. 4.7 - Prob. 125E Ch. 4.7 - Prob. 126E Ch. 4.7 - Prob. 127E Ch. 4.7 - Prob. 128E Ch. 4.7 - Prob. 129E Ch. 4.7 - Prob. 130E Ch. 4.8 - Prob. 1E Ch. 4.8 - Prob. 2E Ch. 4.8 - Prob. 3E Ch. 4.8 - Prob. 4E Ch. 4.8 - Prob. 5E Ch. 4.8 - Prob. 6E Ch. 4.8 - Prob. 7E Ch. 4.8 - Prob. 8E Ch. 4.8 - Prob. 9E Ch. 4.8 - Prob. 10E Ch. 4.8 - Prob. 11E Ch. 4.8 - Prob. 12E Ch. 4.8 - Prob. 13E Ch. 4.8 - Prob. 14E Ch. 4.8 - Prob. 15E Ch. 4.8 - Prob. 16E Ch. 4.8 - Prob. 17E Ch. 4.8 - Prob. 18E Ch. 4.8 - Prob. 19E Ch. 4.8 - Prob. 20E Ch. 4.8 - Prob. 21E Ch. 4.8 - Prob. 22E Ch. 4.8 - Prob. 23E Ch. 4.8 - Prob. 24E Ch. 4.8 - Prob. 25E Ch. 4.8 - Prob. 26E Ch. 4.8 - Prob. 27E Ch. 4.8 - Prob. 28E Ch. 4.8 - Prob. 29E Ch. 4.8 - Prob. 30E Ch. 4.8 - Prob. 31E Ch. 4.8 - Prob. 32E Ch. 4.8 - Prob. 33E Ch. 4.8 - Prob. 34E Ch. 4.8 - Prob. 35E Ch. 4.8 - Prob. 36E Ch. 4.8 - Prob. 37E Ch. 4.8 - Prob. 38E Ch. 4.8 - Prob. 39E Ch. 4.8 - Prob. 40E Ch. 4.8 - Prob. 41E Ch. 4.8 - Prob. 42E Ch. 4.8 - Prob. 43E Ch. 4.8 - Prob. 44E Ch. 4.8 - Prob. 45E Ch. 4.8 - Prob. 46E Ch. 4.8 - Prob. 47E Ch. 4.8 - Prob. 48E Ch. 4.8 - Prob. 49E Ch. 4.8 - Prob. 50E Ch. 4.8 - Prob. 51E Ch. 4.8 - Prob. 52E Ch. 4.8 - Prob. 53E Ch. 4.8 - Prob. 54E Ch. 4.8 - Prob. 55E Ch. 4.8 - Prob. 56E Ch. 4.8 - Prob. 57E Ch. 4.8 - Prob. 58E Ch. 4.8 - Prob. 59E Ch. 4.8 - Prob. 60E Ch. 4 - Prob. 1RE Ch. 4 - Prob. 2RE Ch. 4 - Prob. 3RE Ch. 4 - Prob. 4RE Ch. 4 - Prob. 5RE Ch. 4 - Prob. 6RE Ch. 4 - Prob. 7RE Ch. 4 - Prob. 8RE Ch. 4 - Prob. 9RE Ch. 4 - Prob. 10RE Ch. 4 - Prob. 11RE Ch. 4 - Prob. 12RE Ch. 4 - Prob. 13RE Ch. 4 - Prob. 14RE Ch. 4 - Prob. 15RE Ch. 4 - Prob. 16RE Ch. 4 - Prob. 17RE Ch. 4 - Prob. 18RE Ch. 4 - Prob. 19RE Ch. 4 - Prob. 20RE Ch. 4 - Prob. 21RE Ch. 4 - Prob. 22RE Ch. 4 - Prob. 23RE Ch. 4 - Prob. 24RE Ch. 4 - Prob. 25RE Ch. 4 - Prob. 26RE Ch. 4 - Prob. 27RE Ch. 4 - Prob. 28RE Ch. 4 - Prob. 29RE Ch. 4 - Prob. 30RE Ch. 4 - Prob. 31RE Ch. 4 - Prob. 32RE Ch. 4 - Prob. 33RE Ch. 4 - Prob. 34RE Ch. 4 - Prob. 35RE Ch. 4 - Prob. 36RE Ch. 4 - Prob. 37RE Ch. 4 - Prob. 38RE Ch. 4 - Prob. 39RE Ch. 4 - Prob. 40RE Ch. 4 - Prob. 41RE Ch. 4 - Prob. 42RE Ch. 4 - Prob. 43RE Ch. 4 - Prob. 44RE Ch. 4 - Prob. 45RE Ch. 4 - Prob. 46RE Ch. 4 - Prob. 47RE Ch. 4 - Prob. 48RE Ch. 4 - Prob. 49RE Ch. 4 - Prob. 50RE Ch. 4 - Prob. 51RE Ch. 4 - Prob. 52RE Ch. 4 - Prob. 53RE Ch. 4 - Prob. 54RE Ch. 4 - Prob. 55RE Ch. 4 - Prob. 56RE Ch. 4 - Prob. 57RE Ch. 4 - Prob. 58RE Ch. 4 - Prob. 59RE Ch. 4 - Prob. 60RE Ch. 4 - Prob. 61RE Ch. 4 - Prob. 62RE Ch. 4 - Prob. 63RE Ch. 4 - Prob. 64RE Ch. 4 - Prob. 65RE Ch. 4 - Prob. 66RE Ch. 4 - Prob. 67RE Ch. 4 - Prob. 68RE Ch. 4 - Prob. 69RE Ch. 4 - Prob. 70RE Ch. 4 - Prob. 71RE Ch. 4 - Prob. 72RE Ch. 4 - Prob. 73RE Ch. 4 - Prob. 74RE Ch. 4 - Prob. 75RE Ch. 4 - Prob. 76RE Ch. 4 - Prob. 77RE Ch. 4 - Prob. 78RE Ch. 4 - Prob. 79RE Ch. 4 - Prob. 80RE Ch. 4 - Prob. 81RE Ch. 4 - Prob. 82RE Ch. 4 - Prob. 83RE Ch. 4 - Prob. 84RE Ch. 4 - Prob. 85RE Ch. 4 - Prob. 86RE Ch. 4 - Prob. 87RE Ch. 4 - Prob. 88RE Ch. 4 - Prob. 89RE Ch. 4 - Prob. 90RE Ch. 4 - Prob. 91RE Ch. 4 - Prob. 92RE Ch. 4 - Prob. 93RE Ch. 4 - Prob. 94RE Ch. 4 - Prob. 95RE Ch. 4 - Prob. 96RE Ch. 4 - Prob. 97RE Ch. 4 - Prob. 98RE Ch. 4 - Prob. 99RE Ch. 4 - Prob. 100RE Ch. 4 - Prob. 101RE Ch. 4 - Prob. 102RE Ch. 4 - Prob. 1CT Ch. 4 - Prob. 2CT Ch. 4 - Prob. 3CT Ch. 4 - Prob. 4CT Ch. 4 - Prob. 5CT Ch. 4 - Prob. 6CT Ch. 4 - Prob. 7CT Ch. 4 - Prob. 8CT Ch. 4 - Prob. 9CT Ch. 4 - Prob. 10CT Ch. 4 - Prob. 11CT Ch. 4 - Prob. 12CT Ch. 4 - Prob. 13CT Ch. 4 - Prob. 14CT Ch. 4 - Prob. 15CT Ch. 4 - Prob. 16CT Ch. 4 - Prob. 17CT Ch. 4 - Prob. 18CT Ch. 4 - Prob. 19CT Ch. 4 - Prob. 20CT Ch. 4 - Prob. 1PS Ch. 4 - Prob. 2PS Ch. 4 - Prob. 3PS Ch. 4 - Prob. 4PS Ch. 4 - Prob. 5PS Ch. 4 - Prob. 6PS Ch. 4 - Prob. 7PS Ch. 4 - Prob. 8PS Ch. 4 - Prob. 9PS Ch. 4 - Prob. 10PS Ch. 4 - Prob. 11PS Ch. 4 - Prob. 12PS Ch. 4 - Prob. 13PS Ch. 4 - Prob. 14PS

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