/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 A ladder that is 20 feet long le... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 21

A ladder that is 20 feet long leans against the side of a house. The angle of elevation of the ladder is \(80^{\circ} .\) Find the height from the top of the ladder to the ground.

Short Answer

Expert verified
The height from the top of the ladder to the ground is approximately 19.72 feet.

Step by step solution

01

Identify known values and unknowns

We know the hypotenuse of the right triangle (20 feet) and the angle of elevation \(80^{\circ}\). We're looking for the height from the top of the ladder (the opposite side of the triangle) to the ground.
02

Apply the sine function

Since the sine of an angle in a right angled triangle is defined as the ratio of the length of the side opposite to the given angle to the hypotenuse, we can write the equation as \( \sin(80^{\circ}) = \frac{opposite}{hypotenuse} \) which simplifies to \( \sin(80^{\circ}) = \frac{height}{20 feet}\).
03

Solve the equation

To find the height, we multiply both sides of the equation by 20 feet. This gives us the equation height = \(20 feet * \sin(80^{\circ})\).
04

Calculate the result

Now we calculate this value using a calculator set to degree mode to find the value of \( \sin(80^{\circ})\) and multiply it by 20 to get the height to the nearest foot.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Sketch a graph of the function and compare the graph of \(g\) with the graph of \(f(x)=\arcsin x\). $$g(x)=\arcsin (x-1)$$

Define the inverse cotangent function by restricting the domain of the cotangent function to the interval \((0, \pi),\) and sketch the graph of the inverse trigonometric function.

True or False? Determine whether the statement is true or false. Justify your answer. The difference between the measures of two coterminal angles is always a multiple of \(360^{\circ}\) when expressed in degrees and is always a multiple of \(2 \pi\) radians when expressed in radians.

Graph the functions \(f\) and \(g .\) Use the graphs to make a conjecture about the relationship between the functions. $$f(x)=\cos ^{2} \frac{\pi x}{2}, \quad g(x)=\frac{1}{2}(1+\cos \pi x)$$

Use a graphing utility to graph the function. $$f(x)=\frac{\pi}{2}+\cos ^{-1}\left(\frac{1}{\pi}\right)$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.