   Chapter 8.2, Problem 76E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Empire State Building You are standing 45 meters from the base of the Empire State Building. You estimate that the angle of elevation to the top of the 86th floor is 82°. The total height of the building is another 123 meters above the 86th floor.(a) What is the approximate height of the building?(b) One of your friends is on the 86th floor. What is the distance between you and your friend?

(a)

To determine

To calculate: The approximate height of the building h when the angle of elevation is 82° from the 86th floor and the height of the building is 123 meter more from 86th floor.

Explanation

Given Information:

The angle of elevation to the top of the 86th floor is 82°, the total height of building is 123 meters above the 86th floor.

The distance between observer and base of building is 45 meters.

Formula used:

The definition of tangent,

tanθ=yx

Where, x is the length of the side adjacent to θ, y is the length of the side opposite to θ, and r=x2+y2 is the length of hypotenuse which is not equal to 0.

Calculation:

Consider the given data,

The angle of elevation to the top of the 86th floor is 82°, the total height of building is 123 meters above the 86th floor. The distance between observer and base of building is 45 meters.

Let the approximate height of the building h and distance between base and 86th floor is x.

Now draw the diagram of given situation,

(b)

To determine

To calculate: The distance d between you and your friend who is on the 86th floor.

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