To estimate the height of the totem pole. Jorge used a small square of plastic. He holds the square up to his eyes and walks backward from the pole. He stops when the bottom of the pole lines up with the bottom edge of the square and the top of the pole lines up with the top edge of the square. Jorge’s eye level is about 2 m from the ground. He is about 3 m from the pole. Which is the best estimate for the height of the totem pole? A. 4.5cm B. 5 m C. 6.5 m D: 9 m
To estimate the height of the totem pole. Jorge used a small square of plastic. He holds the square up to his eyes and walks backward from the pole. He stops when the bottom of the pole lines up with the bottom edge of the square and the top of the pole lines up with the top edge of the square. Jorge’s eye level is about 2 m from the ground. He is about 3 m from the pole. Which is the best estimate for the height of the totem pole? A. 4.5cm B. 5 m C. 6.5 m D: 9 m
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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To estimate the height of the totem pole. Jorge used a small square of plastic. He holds the square up to his eyes and walks backward from the pole. He stops when the bottom of the pole lines up with the bottom edge of the square and the top of the pole lines up with the top edge of the square. Jorge’s eye level is about 2 m from the ground. He is about 3 m from the pole.
Which is the best estimate for the height of the totem pole?
A. 4.5cm
B. 5 m
C. 6.5 m
D: 9 m
![**Determining the Height of an Object Using Triangulation**
*Concept Overview*:
This illustration demonstrates how you can use basic trigonometry and triangulation to determine the height of a tall object, such as a totem pole, using the principle of similar triangles.
*Description of the Diagram*:
In the diagram, an observer is using a triangulation instrument to measure the height of a totem pole. There are two significant distances and one angle involved:
1. **Observer's Distance from the Totem Pole**: The observer is standing 5 meters away from the base of the totem pole.
2. **Height of the Observer's Viewpoint**: The line of sight from the observer's eyes to the top of the totem pole creates two triangles:
- The smaller right triangle where the height from the ground to the observer's eyes is given as 1.5 meters.
- The larger right triangle from the observer's eyes to the top of the totem pole includes the height of the totem pole.
*Procedure to Calculate the Totem Pole's Height*:
1. Measure the angle between the observer's line of sight to the top of the totem pole and the ground.
2. Use this angle to form right triangles:
- **Right Triangle Formed by the Observer's Instrument**: Base is the distance from the observer to the totem pole (5 meters), and the height is from the observer's eyes (1.5 m).
- **Overall Height Triangle of the Totem Pole**: Base remains 5 meters, and the height you want to find is the total height of the totem pole.
*Step-by-Step Calculation*:
- Let's assume the angle measured by the instrument is θ.
- Use the trigonometric tangent function, which relates the angle of elevation (θ) to the ratio of the opposite side (the object's height minus the observer's height) over the adjacent side (distance from the observer to the object's base).
\[
\tan(θ) = \frac{\text{totem pole height - observer's height}}{\text{distance to the totem pole}}
\]
\[
\tan(θ) = \frac{h - 1.5 \, \text{m}}{5 \, \text{m}}
\]
- Rearrange to solve for the height (h) of the totem pole:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64623b0f-3175-4011-bf32-b2f0324443cb%2Fcde5ec9c-9a0e-4125-9937-6c1221e03f84%2F2cm4nqi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determining the Height of an Object Using Triangulation**
*Concept Overview*:
This illustration demonstrates how you can use basic trigonometry and triangulation to determine the height of a tall object, such as a totem pole, using the principle of similar triangles.
*Description of the Diagram*:
In the diagram, an observer is using a triangulation instrument to measure the height of a totem pole. There are two significant distances and one angle involved:
1. **Observer's Distance from the Totem Pole**: The observer is standing 5 meters away from the base of the totem pole.
2. **Height of the Observer's Viewpoint**: The line of sight from the observer's eyes to the top of the totem pole creates two triangles:
- The smaller right triangle where the height from the ground to the observer's eyes is given as 1.5 meters.
- The larger right triangle from the observer's eyes to the top of the totem pole includes the height of the totem pole.
*Procedure to Calculate the Totem Pole's Height*:
1. Measure the angle between the observer's line of sight to the top of the totem pole and the ground.
2. Use this angle to form right triangles:
- **Right Triangle Formed by the Observer's Instrument**: Base is the distance from the observer to the totem pole (5 meters), and the height is from the observer's eyes (1.5 m).
- **Overall Height Triangle of the Totem Pole**: Base remains 5 meters, and the height you want to find is the total height of the totem pole.
*Step-by-Step Calculation*:
- Let's assume the angle measured by the instrument is θ.
- Use the trigonometric tangent function, which relates the angle of elevation (θ) to the ratio of the opposite side (the object's height minus the observer's height) over the adjacent side (distance from the observer to the object's base).
\[
\tan(θ) = \frac{\text{totem pole height - observer's height}}{\text{distance to the totem pole}}
\]
\[
\tan(θ) = \frac{h - 1.5 \, \text{m}}{5 \, \text{m}}
\]
- Rearrange to solve for the height (h) of the totem pole:
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