To determine To find: a. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 100 feet from the base of the tower? Answer a. Therefore of the guy wire that is secured on the top is 492.6 ft. Explanation Given: The height of a radio tower is 500 feet, and the ground on one side of the tower slopes upward at an angle of 10 ° (see the figure). Formula used: c 2 = a 2 + b 2 − 2 a b cos C Calculation: a. Let x be length of the guy wire that is secured on the slope. x ² = 500 ² + 100 ² − 2 * 500 * 100 * cos ( 90 ° − 10 ° ) x = 500 2 + 100 2 − 100000 cos 80 x ≈ 492.6 Therefore of the guy wire that is secured on the top is 492.6 ft. To determine To find: b. How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a position 100 feet from the base on the flat side? Answer b. The length of the guy wire that is secured in the middle is 269.3 feet. Explanation Given: The height of a radio tower is 500 feet, and the ground on one side of the tower slopes upward at an angle of 10 ° (see the figure). Formula used: c 2 = a 2 + b 2 − 2 a b cos C Calculation: b. Let y be length of the guy wire that is secured in the middle. y ² = 100 ² + ( 500 2 ) 2 − 2 * 100 * ( 500 2 ) cos 90 y = 10000 + 62500 y = 269.3 The length of the guy wire that is secured in the middle is 269.3 feet.

9th Edition

ISBN: 9780321716835

Author: Michael Sullivan

Publisher: Addison Wesley

See similar textbooks

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.

Videos

Textbook Question

Chapter 8.3, Problem 49AYU

Finding the Length of a Guy Wire The height of a radi tower is 500 feet, and the ground on one side of the tower slopes upward at an angle of $10^{\circ}$ (see the figure).

a. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the slope side 100 feet from the base of the tower?

b. How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a positio 100 feet from the baseon the flat side?

Chapter 8.3, Problem 49AYU, Finding the Length of a Guy Wire The height of a radi tower is 500 feet, and the ground on one side

Expert Solution

To determine

To find:

a. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 100 feet from the base of the tower?

Answer to Problem 49AYU

a. Therefore of the guy wire that is secured on the top is $492.6$ ft.

Explanation of Solution

Given:

The height of a radio tower is 500 feet, and the ground on one side of the tower slopes upward at an angle of $10 °$ (see the figure).

Precalculus, Chapter 8.3, Problem 49AYU , additional homework tip 1

Formula used:

$c^{2} = a^{2} + b^{2} - 2 a b cos C$

Calculation:

Precalculus, Chapter 8.3, Problem 49AYU , additional homework tip 2

a. Let $x$ be length of the guy wire that is secured on the slope.

$x ² = 500 ² + 100 ² - 2 * 500 * 100 * cos (90 ° - 10 °)$

$x = \sqrt{500^{2} + 100^{2} - 100000 cos 80}$

$x \approx 492.6$

Therefore of the guy wire that is secured on the top is $492.6$ ft.

Expert Solution

To determine

To find:

b. How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a position 100 feet from the base on the flat side?

Answer to Problem 49AYU

b. The length of the guy wire that is secured in the middle is $269.3$ feet.

Explanation of Solution

Given:

The height of a radio tower is 500 feet, and the ground on one side of the tower slopes upward at an angle of $10 °$ (see the figure).

Precalculus, Chapter 8.3, Problem 49AYU , additional homework tip 3

Formula used:

$c^{2} = a^{2} + b^{2} - 2 a b cos C$

Calculation:

Precalculus, Chapter 8.3, Problem 49AYU , additional homework tip 4

b. Let $y$ be length of the guy wire that is secured in the middle.

$y ² = 100 ² + {(\frac{500}{2})}^{2} - 2 * 100 * (\frac{500}{2}) \cos 90$

$y = \sqrt{10000 + 62500}$

$y = 269.3$

The length of the guy wire that is secured in the middle is $269.3$ feet.

Chapter 8.3, Problem 48AYU

Chapter 8.3, Problem 50AYU

Chapter 8 Solutions

Precalculus

Ch. 8.1 - In a right triangle, if the length of the...Ch. 8.1 - If is an acute angle, solve the equation tan= 1 2...Ch. 8.1 - If is an acute angle, solve the equation sin= 1 2...Ch. 8.1 - True or False sin 52 =cos 48 Ch. 8.1 - Prob. 5AYU Ch. 8.1 - When you look up at an object, the acute angle...Ch. 8.1 - Prob. 7AYU Ch. 8.1 - Prob. 8AYU Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - In Problems 9-18, find the exact value of the six...

Additional Math Textbook Solutions

Find more solutions based on key concepts

For a population containing N=902 individual, what code number would you assign for a. the first person on the ...

Basic Business Statistics, Student Value Edition

Interpreting a P-Value In Exercises 3–8, the P-value for a hypothesis test is shown. Use the P-value to decide ...

Elementary Statistics: Picturing the World (7th Edition)

Trigonometric substitutions Evaluate the following integrals. 17. 64x2dx

Calculus: Early Transcendentals (2nd Edition)

Calculate the area of given figure.

Pre-Algebra Student Edition

The table by using the given graph of h.

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

CHECK POINT 1 Find a counterexample to show that the statement The product of two two-digit numbers is a three-...

Thinking Mathematically (6th Edition)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Solution Summary: The author explains how long a guy wire should be if it is to connect to the top of the tower and be secured 100 feet from the base on the flat side.

Concept explainers

Videos

Answer to Problem 49AYU

Explanation of Solution

Answer to Problem 49AYU

Explanation of Solution

Chapter 8 Solutions

Additional Math Textbook Solutions