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 5.4, Problem 25E

(a)

To determine

To draw: A labeled diagram of the situation.

(a)

Expert Solution

Answer to Problem 25E

The diagram

Explanation of Solution

Given information: Fire Fighting: The longest truck-mounted ladder used by the Dallas Fire Department is 108 feet long and consists of four hydraulic sections. Gerald Travis, aerial expert for the department, indicates that the optimum operating angle of this ladder is 60∘ . The fire fighters find they need to reach the roof of an 84-foot burning building. Assume the ladder is mounted 8 feet above the ground.

Calculation:

Labeled diagram

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.4, Problem 25E , additional homework tip 1

(b)

To determine

To find: far building should the base of the ladder be placed to achieve the optimum operating angle.

(b)

Expert Solution

Answer to Problem 25E

43.9 feet

Explanation of Solution

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.4, Problem 25E , additional homework tip 2

The goal is to determine the distance BC = x :

We have

tan60∘=ABBC=84−8x=76x→x=76tan60∘x=43.9 feet

Thus, it should be 43.9 feet far.

(c)

To determine

To find: distance to which ladder be extended to reach the roof.

(c)

Expert Solution

Answer to Problem 25E

87.8 feet

Explanation of Solution

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.4, Problem 25E , additional homework tip 3

The goal is to determine the distance AC

We have

sin60∘=ABAC=76ACAC=76sin60∘AC=87.8 feet

Thus, it should be extended to 87.8 feet to reach the roof.

Chapter 5.4, Problem 24E

Chapter 5.4, Problem 26E

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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