1) If the angle of elevation of the sun is 63.4° when a building casts a shadow of 37.5 feet, what is the height of the building? You must show all your work and your answer need to include a drawing.
1) If the angle of elevation of the sun is 63.4° when a building casts a shadow of 37.5 feet, what is the height of the building? You must show all your work and your answer need to include a drawing.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Problem Overview:**
1) If the angle of elevation of the sun is 63.4° when a building casts a shadow of 37.5 feet, what is the height of the building? You must show all your work, and your answer needs to include a drawing.
---
**Solution Explanation:**
To find the height of the building, you can use trigonometry. The angle of elevation is the angle between the line of sight from the tip of the shadow to the top of the building and the ground. This forms a right triangle where:
- The shadow is the adjacent side.
- The height of the building is the opposite side.
- The angle of elevation is given as 63.4°.
**Steps to Solve:**
1. Use the tangent function, which relates the opposite side (height of the building) to the adjacent side (length of the shadow):
\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\]
2. Plug in the known values:
\[
\tan(63.4^\circ) = \frac{\text{height}}{37.5}
\]
3. Solve for the height of the building:
\[
\text{height} = 37.5 \times \tan(63.4^\circ)
\]
4. Calculate the value:
- Use a calculator to find \(\tan(63.4^\circ)\).
- Multiply the result by 37.5 to find the height.
**Include a Drawing:**
Make sure to include a right triangle diagram with:
- The base labeled as the shadow (37.5 feet).
- The vertical side labeled as the height of the building.
- The angle of elevation (63.4°) clearly marked between the base and the hypotenuse (line of sight).
This illustration helps visualize the problem and demonstrates the trigonometric relationships in context.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe708b20e-246d-43f9-aec0-b076b54d250e%2Fa7d5c6d3-e027-4838-ba00-6832cade9fb3%2Fzlu8c2u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Overview:**
1) If the angle of elevation of the sun is 63.4° when a building casts a shadow of 37.5 feet, what is the height of the building? You must show all your work, and your answer needs to include a drawing.
---
**Solution Explanation:**
To find the height of the building, you can use trigonometry. The angle of elevation is the angle between the line of sight from the tip of the shadow to the top of the building and the ground. This forms a right triangle where:
- The shadow is the adjacent side.
- The height of the building is the opposite side.
- The angle of elevation is given as 63.4°.
**Steps to Solve:**
1. Use the tangent function, which relates the opposite side (height of the building) to the adjacent side (length of the shadow):
\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\]
2. Plug in the known values:
\[
\tan(63.4^\circ) = \frac{\text{height}}{37.5}
\]
3. Solve for the height of the building:
\[
\text{height} = 37.5 \times \tan(63.4^\circ)
\]
4. Calculate the value:
- Use a calculator to find \(\tan(63.4^\circ)\).
- Multiply the result by 37.5 to find the height.
**Include a Drawing:**
Make sure to include a right triangle diagram with:
- The base labeled as the shadow (37.5 feet).
- The vertical side labeled as the height of the building.
- The angle of elevation (63.4°) clearly marked between the base and the hypotenuse (line of sight).
This illustration helps visualize the problem and demonstrates the trigonometric relationships in context.
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