/*! 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

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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.

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