David is looking out of his window at the office building 40 feet away across the street from him. He determines that the angle of elevation to the top of the building is 62° and the angle of depression to the bottom of the building is 55°. How tall, to the nearest foot, is the office building? Do not include units in your answer.
David is looking out of his window at the office building 40 feet away across the street from him. He determines that the angle of elevation to the top of the building is 62° and the angle of depression to the bottom of the building is 55°. How tall, to the nearest foot, is the office building? Do not include units in your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![**Question**
David is looking out of his window at the office building 40 feet away across the street from him. He determines that the angle of elevation to the top of the building is 62° and the angle of depression to the bottom of the building is 55°. How tall, to the nearest foot, is the office building? Do not include units in your answer.
**Provide your answer below:**
[Answer box for user input]
**Explanation**
In this problem, David uses trigonometry to calculate the height of an office building. He uses the angles of elevation and depression from his window to determine the total height of the building. The angle of elevation is the angle between the horizontal line from David's position and the line of sight to the top of the building. Similarly, the angle of depression is the angle between the horizontal line and the line of sight to the bottom of the building.
Using these two angles, along with the known distance across the street, allows us to calculate the height of the building using trigonometric functions such as tangent. The tangent function relates an angle in a right triangle to the ratio of the opposite side (height of the building, in this case) to the adjacent side (the distance across the street).
Note that no graph or diagram is provided in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71104923-f5df-4d9c-a2c5-407c8762d11b%2F6a4f04b0-af41-42f6-b457-db610771dc74%2Fdv2prg.jpeg&w=3840&q=75)
Transcribed Image Text:**Question**
David is looking out of his window at the office building 40 feet away across the street from him. He determines that the angle of elevation to the top of the building is 62° and the angle of depression to the bottom of the building is 55°. How tall, to the nearest foot, is the office building? Do not include units in your answer.
**Provide your answer below:**
[Answer box for user input]
**Explanation**
In this problem, David uses trigonometry to calculate the height of an office building. He uses the angles of elevation and depression from his window to determine the total height of the building. The angle of elevation is the angle between the horizontal line from David's position and the line of sight to the top of the building. Similarly, the angle of depression is the angle between the horizontal line and the line of sight to the bottom of the building.
Using these two angles, along with the known distance across the street, allows us to calculate the height of the building using trigonometric functions such as tangent. The tangent function relates an angle in a right triangle to the ratio of the opposite side (height of the building, in this case) to the adjacent side (the distance across the street).
Note that no graph or diagram is provided in the image.
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