Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Concept explainers

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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Question

Chapter 5.6, Problem 32E

To determine

To find: The length of the track.

Expert Solution & Answer

Answer to Problem 32E

807.7 feet

Explanation of Solution

Given information: Cable Cars: The Duquesne Incline is a cable car in Pittsburgh, Pennsylvania, which transports passengers up and down a mountain. The track used by the cable car has an angle of elevation of 30∘ . The angle of elevation to the top of the track from a point that is horizontally 100 feet from the base of the track is about 26.8∘ .

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.6, Problem 32E , additional homework tip 1

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.6, Problem 32E , additional homework tip 2

This is the sketch. We can use the 30 degree angle to figure out that the obtuse angle of the triangle is 150∘ since they form a linear pair. We can then find the third, acute angle at the top by subtracting these two from 180 degree is:

180∘−(150∘+26.8∘)=3.2∘

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.6, Problem 32E , additional homework tip 3

Here is a simplified view, we are looking for the length of the track which is labeled t , and we can set up a ratio using the law of sines,

100sin3.2∘=tsin26.8∘t=100×sin26.8∘sin3.2∘t=807.7

Thus, the length of the track is 807.7 feet.

Chapter 5.6, Problem 31E

Chapter 5.6, Problem 33E

Chapter 5 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 5.1 - Prob. 1CFU Ch. 5.1 - Prob. 2CFU Ch. 5.1 - Prob. 3CFU Ch. 5.1 - Prob. 4CFU Ch. 5.1 - Prob. 5CFU Ch. 5.1 - Prob. 6CFU Ch. 5.1 - Prob. 7CFU Ch. 5.1 - Prob. 8CFU Ch. 5.1 - Prob. 9CFU Ch. 5.1 - Prob. 10CFU

Ch. 5.1 - Prob. 11CFU Ch. 5.1 - Prob. 12CFU Ch. 5.1 - Prob. 13CFU Ch. 5.1 - Prob. 14CFU Ch. 5.1 - Prob. 15CFU Ch. 5.1 - Prob. 16CFU Ch. 5.1 - Prob. 17CFU Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.1 - Prob. 59E Ch. 5.1 - 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Prob. 2GCE Ch. 5.8B - Prob. 3GCE Ch. 5.8B - Prob. 4GCE Ch. 5 - Prob. 1SGA Ch. 5 - Prob. 2SGA Ch. 5 - Prob. 3SGA Ch. 5 - Prob. 4SGA Ch. 5 - Prob. 5SGA Ch. 5 - Prob. 6SGA Ch. 5 - Prob. 7SGA Ch. 5 - Prob. 8SGA Ch. 5 - Prob. 9SGA Ch. 5 - Prob. 10SGA Ch. 5 - Prob. 11SGA Ch. 5 - Prob. 12SGA Ch. 5 - Prob. 13SGA Ch. 5 - Prob. 14SGA Ch. 5 - Prob. 15SGA Ch. 5 - Prob. 16SGA Ch. 5 - Prob. 17SGA Ch. 5 - Prob. 18SGA Ch. 5 - Prob. 19SGA Ch. 5 - Prob. 20SGA Ch. 5 - Prob. 21SGA Ch. 5 - Prob. 22SGA Ch. 5 - Prob. 23SGA Ch. 5 - Prob. 24SGA Ch. 5 - Prob. 25SGA Ch. 5 - Prob. 26SGA Ch. 5 - Prob. 27SGA Ch. 5 - Prob. 28SGA Ch. 5 - Prob. 29SGA Ch. 5 - Prob. 30SGA Ch. 5 - Prob. 31SGA Ch. 5 - Prob. 32SGA Ch. 5 - Prob. 33SGA Ch. 5 - Prob. 34SGA Ch. 5 - Prob. 35SGA Ch. 5 - Prob. 36SGA Ch. 5 - Prob. 37SGA Ch. 5 - Prob. 38SGA Ch. 5 - Prob. 39SGA Ch. 5 - Prob. 40SGA Ch. 5 - Prob. 41SGA Ch. 5 - Prob. 42SGA Ch. 5 - Prob. 43SGA Ch. 5 - Prob. 44SGA Ch. 5 - Prob. 45SGA Ch. 5 - Prob. 46SGA Ch. 5 - Prob. 47SGA Ch. 5 - Prob. 48SGA Ch. 5 - 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