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
Related questions
Question
29. Using the diagram find the measurement of GF.
![### Question 29: Using the diagram find the measurement of GF
Below is the provided diagram of a right triangle labeled \( \triangle GFH \):
- \( \angle FGH \) is a right angle (90°).
- \( \angle FHG \) is given as 35°.
- The length of \( FH \) (the hypotenuse) is 18.4 inches.
You are required to find the measurement of \( GF \) (the side opposite to \( \angle FHG \)).
#### Diagram Analysis:
```
G
*
/|
/ |
/ |
/ |
/ |
/ |
90° / | 35°
/ |
/ |
GF / |
/___________|
F H
18.4 in.
```
#### The Options:
- \( A \) 22.46
- \( B \) 15.07
- \( C \) 12.88
- \( D \) 10.55
To calculate the length of \( GF \), we can use the sine function related to the 35° angle since sine relates the opposite side to the hypotenuse in a right triangle:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Thus:
\[ \sin(35^\circ) = \frac{GF}{18.4 \text{ in.}} \]
Rearranging this formula to solve for \( GF \):
\[ GF = 18.4 \, \text{in.} \cdot \sin(35^\circ) \]
Using a calculator to find the sine of 35°:
\[ \sin(35^\circ) \approx 0.5736 \]
\[ GF = 18.4 \, \text{in.} \cdot 0.5736 \]
\[ GF \approx 10.55 \, \text{in.} \]
Hence, the length of \( GF \) is approximately 10.55 inches.
#### Correct Answer:
- \( D \) 10.55](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34bff1e1-af68-4229-b0ef-aa0aaa134e46%2F9fd5e45a-c28c-4c9d-80b7-735e4a89725c%2Fe9hn17_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 29: Using the diagram find the measurement of GF
Below is the provided diagram of a right triangle labeled \( \triangle GFH \):
- \( \angle FGH \) is a right angle (90°).
- \( \angle FHG \) is given as 35°.
- The length of \( FH \) (the hypotenuse) is 18.4 inches.
You are required to find the measurement of \( GF \) (the side opposite to \( \angle FHG \)).
#### Diagram Analysis:
```
G
*
/|
/ |
/ |
/ |
/ |
/ |
90° / | 35°
/ |
/ |
GF / |
/___________|
F H
18.4 in.
```
#### The Options:
- \( A \) 22.46
- \( B \) 15.07
- \( C \) 12.88
- \( D \) 10.55
To calculate the length of \( GF \), we can use the sine function related to the 35° angle since sine relates the opposite side to the hypotenuse in a right triangle:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Thus:
\[ \sin(35^\circ) = \frac{GF}{18.4 \text{ in.}} \]
Rearranging this formula to solve for \( GF \):
\[ GF = 18.4 \, \text{in.} \cdot \sin(35^\circ) \]
Using a calculator to find the sine of 35°:
\[ \sin(35^\circ) \approx 0.5736 \]
\[ GF = 18.4 \, \text{in.} \cdot 0.5736 \]
\[ GF \approx 10.55 \, \text{in.} \]
Hence, the length of \( GF \) is approximately 10.55 inches.
#### Correct Answer:
- \( D \) 10.55
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