Building 68 120 ft Note: Figure is not drawn to scale. 68° is the angle of el, 120 ft. is the; and the height of the building is the; So, use feet tall (to the nearest whole i to solve for the height of the building. The building is foot).
Building 68 120 ft Note: Figure is not drawn to scale. 68° is the angle of el, 120 ft. is the; and the height of the building is the; So, use feet tall (to the nearest whole i to solve for the height of the building. The building is foot).
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
![### Solving the Height of a Building Using Trigonometry
#### Problem Statement:
A right triangle is presented where:
- The horizontal distance from the observer to the base of a building is 120 feet.
- The angle of elevation from the observer to the top of the building is 68 degrees.
The objective is to find the height of the building.
#### Diagram Description:
The provided diagram is a right triangle with:
- The angle of elevation at 68 degrees.
- The adjacent side (horizontal distance) labeled as 120 feet.
- The opposite side (height of the building) is the unknown.
*Note: The figure is not drawn to scale.*
#### Solution Steps:
1. Identify known values:
- The angle of elevation (θ) is 68 degrees.
- The adjacent side (adjacent to θ) is 120 feet.
- The opposite side (opposite to θ) is the height of the building (unknown).
2. Set up the trigonometric relationship:
- The tangent function (tan) relates the opposite side to the adjacent side.
- \[\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\]
3. Substitute the known values into the equation:
- \[\tan(68^\circ) = \frac{\text{height}}{120}\]
4. Solve for the height of the building:
- \[\text{height} = 120 \times \tan(68^\circ)\]
5. Use a calculator to find \(\tan(68^\circ)\):
- \[\tan(68^\circ) \approx 2.4751\]
6. Multiply to find the height:
- \[\text{height} = 120 \times 2.4751 \approx 297\]
#### Conclusion:
The height of the building is approximately 297 feet.
---
#### Fill in the Blanks (for educational exercise):
68° is the **angle of elevation**, 120 ft. is the **adjacent side**, and the height of the building is the **opposite side**. So, use **tan** to solve for the height of the building. The building is approximately **297** feet tall (to the nearest whole foot).
---
#### Additional Interactive Elements:
- **\[sin\]** **\[cos\]** **\[tan\]** **\[hypotenuse\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab545a03-1d39-4874-800c-bed9ffa7318e%2F6083fcee-277f-47a6-837a-f2ad65201b39%2Fxi03p3j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving the Height of a Building Using Trigonometry
#### Problem Statement:
A right triangle is presented where:
- The horizontal distance from the observer to the base of a building is 120 feet.
- The angle of elevation from the observer to the top of the building is 68 degrees.
The objective is to find the height of the building.
#### Diagram Description:
The provided diagram is a right triangle with:
- The angle of elevation at 68 degrees.
- The adjacent side (horizontal distance) labeled as 120 feet.
- The opposite side (height of the building) is the unknown.
*Note: The figure is not drawn to scale.*
#### Solution Steps:
1. Identify known values:
- The angle of elevation (θ) is 68 degrees.
- The adjacent side (adjacent to θ) is 120 feet.
- The opposite side (opposite to θ) is the height of the building (unknown).
2. Set up the trigonometric relationship:
- The tangent function (tan) relates the opposite side to the adjacent side.
- \[\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\]
3. Substitute the known values into the equation:
- \[\tan(68^\circ) = \frac{\text{height}}{120}\]
4. Solve for the height of the building:
- \[\text{height} = 120 \times \tan(68^\circ)\]
5. Use a calculator to find \(\tan(68^\circ)\):
- \[\tan(68^\circ) \approx 2.4751\]
6. Multiply to find the height:
- \[\text{height} = 120 \times 2.4751 \approx 297\]
#### Conclusion:
The height of the building is approximately 297 feet.
---
#### Fill in the Blanks (for educational exercise):
68° is the **angle of elevation**, 120 ft. is the **adjacent side**, and the height of the building is the **opposite side**. So, use **tan** to solve for the height of the building. The building is approximately **297** feet tall (to the nearest whole foot).
---
#### Additional Interactive Elements:
- **\[sin\]** **\[cos\]** **\[tan\]** **\[hypotenuse\
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