Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Related questions
Concept explainers
Question
![### Geometry Problem: Calculating the Height of a Kite
**Problem Statement:**
A boy is flying a kite. His kite string is extended 50 meters long. The boy is 1.7 meters tall, and the angle of elevation of the kite to the boy's hands is 12°. How high is the kite flying above the ground?
**Diagram Explanation:**
The diagram illustrates a boy flying a kite. There are several key measurements and angles depicted:
1. **Kite String Length (Hypotenuse)**: The kite string, which is the hypotenuse of the right triangle, is 50 meters long.
2. **Angle of Elevation**: The angle between the string and the horizontal ground is 12°.
3. **Boy's Height**: The height of the boy from the ground to his hands is 1.7 meters.
4. **Vertical Height (x)**: The distance from the boy’s hands to the kite, vertically aligned, is represented as \( x \).
The goal is to determine the total height of the kite above the ground.
**Step-by-Step Solution:**
1. **Establish the Right Triangle**:
- The hypotenuse is 50 meters.
- The angle of elevation is 12°.
2. **Calculate the Vertical Component**:
Using the sine function for the angle of elevation:
\[
\sin(12^\circ) = \frac{\text{Opposite Side (Vertical Component)}}{\text{Hypotenuse (Kite String Length)}}
\]
Let \( h \) be the vertical component from the boy's hands to the kite:
\[
\sin(12^\circ) = \frac{h}{50}
\]
Therefore:
\[
h = 50 \times \sin(12^\circ)
\]
Using a calculator:
\[
h \approx 50 \times 0.2079 \approx 10.395 \text{ meters}
\]
3. **Total Height Above Ground**:
Add the boy's height to the vertical component, \( x \):
\[
\text{Total Height} = h + \text{Boy's Height}
\]
\[
\text{Total Height} \approx 10.395 + 1.7 \approx 12.095 \text{ meters}](https://content.bartleby.com/qna-images/question/c476fe49-bd29-4169-8079-6a3850fe1835/4fc80bcf-0eab-435e-b415-4a86b3f5f2ac/g2j5goj_processed.jpeg)
Transcribed Image Text:### Geometry Problem: Calculating the Height of a Kite
**Problem Statement:**
A boy is flying a kite. His kite string is extended 50 meters long. The boy is 1.7 meters tall, and the angle of elevation of the kite to the boy's hands is 12°. How high is the kite flying above the ground?
**Diagram Explanation:**
The diagram illustrates a boy flying a kite. There are several key measurements and angles depicted:
1. **Kite String Length (Hypotenuse)**: The kite string, which is the hypotenuse of the right triangle, is 50 meters long.
2. **Angle of Elevation**: The angle between the string and the horizontal ground is 12°.
3. **Boy's Height**: The height of the boy from the ground to his hands is 1.7 meters.
4. **Vertical Height (x)**: The distance from the boy’s hands to the kite, vertically aligned, is represented as \( x \).
The goal is to determine the total height of the kite above the ground.
**Step-by-Step Solution:**
1. **Establish the Right Triangle**:
- The hypotenuse is 50 meters.
- The angle of elevation is 12°.
2. **Calculate the Vertical Component**:
Using the sine function for the angle of elevation:
\[
\sin(12^\circ) = \frac{\text{Opposite Side (Vertical Component)}}{\text{Hypotenuse (Kite String Length)}}
\]
Let \( h \) be the vertical component from the boy's hands to the kite:
\[
\sin(12^\circ) = \frac{h}{50}
\]
Therefore:
\[
h = 50 \times \sin(12^\circ)
\]
Using a calculator:
\[
h \approx 50 \times 0.2079 \approx 10.395 \text{ meters}
\]
3. **Total Height Above Ground**:
Add the boy's height to the vertical component, \( x \):
\[
\text{Total Height} = h + \text{Boy's Height}
\]
\[
\text{Total Height} \approx 10.395 + 1.7 \approx 12.095 \text{ meters}
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 4 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Similar questions
- Find the value of Xarrow_forwardA man went off-roading in his Jeep. 40 miles after leaving the highway, he turned left, creating an angle of 95° between the two paths. After another 55 miles he reached the highway again. How much of the highway did he bypass? 95⁰ Round to the nearest hundredth of a mile. He bypassed approximately miles. fo Q Quarrow_forwardFind the value of xarrow_forward
- Find the angle measurement. (3x + 1)° 125°arrow_forwardTwo students are standing 15 feet apart. Between them is a wall. The angle of the student’s foot and the top of the wall is 20° and then 40° to the other student’s foot. How tall is the wall? Round to the nearest hundredth.arrow_forwardAnnie is looking at the top of a tree at an angle of elevation of 40°. She knows that she is 50 feet from the base of the tree. She wants to know how tall the tree is. About how tall is Annie's tree? A 51 feet B 60 feet 55 feet D. 47 feet 78 feet 32 feet 42 feetarrow_forward
- You and your jowa are standing on a field 15 ft away from each other. Between the two of you, there is a floating heart kite. Your angle of elevation to the balloon is 23° and your jowa's angle of elevation to the ballon is 31°. How far is your jowa from the kite? * Your answerarrow_forwardSabri stands 12 feet away from a tree and measures the angle of elevation to the top of the tree to be 56°. Bart is standing behind Sabri and measures the angle to be 51°. a. How high is the tree? b. How far from the tree is Bart? c. How far apart are Bart and Sabri?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Elementary Geometry for College Students
Geometry
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Cengage Learning