Question

Height of a Building The angle of elevation to the top of the Empire State Building in New York is found to be $11^{\circ}$ from the ground at a distance of 1 mi from the base of the building. Using this information, find the height of the Empire State Building.

Name: Problem 53, Chapter 6: Precalculus Mathematics for Calculus
Uploaded: 2020-06-09T18:21:53-08:00
Duration: 1 min 55 s
Channel: Alexandra Ali
Description: Height of a Building The angle of elevation to the top of the Empire State Building in New York is found to be 11^∘ from the ground at a distance of 1 mi from the base of the building. Using this information, find the height of the Empire State Building.

   Height of a Building The angle of elevation to the top of the Empire State Building in New York is found to be $11^{\circ}$ from the ground at a distance of 1 mi from the base of the building. Using this information, find the height of the Empire State Building.

Precalculus Mathematics for Calculus

James Stewart,… 7th Edition

Chapter 6, Problem 53

Instant Answer

Solved by Expert Alexandra Ali

06/09/2020

Step 1

We can use the tangent function to find the height of the building, as the tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, the opposite side is the height of the building (which we are trying to find), and the Show more…

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Height of a Building The angle of elevation to the top of the Empire State Building in New York is found to be $11^{\circ}$ from the ground at a distance of 1 mi from the base of the building. Using this information, find the height of the Empire State Building.

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Key Concepts

Angle of Elevation

The angle of elevation is the angle between the horizontal line from the observer and the line of sight to an object that is above the horizontal. It is commonly used in real-world problems to relate the height of an object to a known distance from the object through trigonometric relationships.

Right Triangle Trigonometry

Right triangle trigonometry is the study of the relationships between the angles and sides of right-angled triangles. In many practical applications, the angles and one side of a triangle are known, allowing the use of trigonometric functions to determine unknown lengths such as height or distance.

Tangent Function

The tangent function, defined as the ratio of the opposite side to the adjacent side in a right triangle, is particularly useful in calculating heights or distances when an angle of elevation or depression is known along with an adjacent distance.

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