/*! 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 41 The Statue of Liberty is approxi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 41

The Statue of Liberty is approximately 305 feet tall. If the angle of elevation of a ship to the top of the statue is \(23.7^{\circ}\), how far, to the nearest foot, is the ship from the statue's base?

Short Answer

Expert verified
The distance from the ship to the statue's base is approximately 708 feet.

Step by step solution

01

Define the Problem in Terms of Trigonometry

We would define the problem in terms of a right triangle, because the height of the statue forms the opposite side of the right angle, and the distance from the base of the statue to the ship forms the adjacent to the angle. The angle of elevation is the angle between the adjacent side and the hypotenuse, which is \(23.7^{\circ}\). Therefore, \(\tan(23.7^{\circ}) = \frac{height}{distance}\), where height is 305 feet and distance is what we're trying to find.
02

Solve for Distance

Rearrange the equation to solve for distance. You should get the following equation: \(distance = \frac{height}{\tan(23.7^{\circ})}\).
03

Substitute the Height of the Statue into the Equation

Now, you can substitute the height of the statue into the equation: \(distance = \frac{305}{\tan(23.7^{\circ})}\).
04

Calculate the Distance to the Nearest Foot

Finally, calculate the distance using a calculator to get an approximate value. Then, round the answer to the nearest foot since the distance is asked in feet.

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

In Exercises 15-20, find the measure of the complement and the supplement of each angle. \(37.4^{\circ}\)

How do you determine whether or not a graph is traversable?

Although the Eiffel Tower in Paris is not a solid pyramid, its shape approximates that of a pyramid with a square base measuring 120 feet on a side and a height of 980 feet. If it were a solid pyramid, what would be the Eiffel Tower's volume, in cubic yards?

Make Sense? In Exercises 56-59, determine whether each statement makes sense or does not make sense, and explain your reasoning. Use a quadratic equation to solve this problem. The width of a rectangular carpet is 7 meters shorter than the length, and the diagonal is 1 meter longer than the length. What are the carpet's dimensions?

If the measure of one of the acute angles and the hypotenuse of a right triangle are known, describe how to find the measure of the remaining parts of the triangle.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.