To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet At approximately what angle does the wire meet the ground? off the ground. The tree meets the ground at a right angle. O 33.6° O39.8° O 50.2° 56.4°
To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet At approximately what angle does the wire meet the ground? off the ground. The tree meets the ground at a right angle. O 33.6° O39.8° O 50.2° 56.4°
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
![### Problem Statement
To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.
**Question:** At approximately what angle does the wire meet the ground?
### Answer Options
- 33.6°
- 39.8°
- 50.2°
- 56.4°
### Explanation
Consider a right triangle formed with:
- the tree as the vertical side (opposite side) measuring 10 feet,
- the ground as the horizontal side (adjacent side), and
- the wire as the hypotenuse measuring 12 feet.
To find the angle θ at which the wire meets the ground, use the trigonometric relationship: sine (sin).
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
\[ \sin(\theta) = \frac{10}{12} \]
First, find the sine value:
\[ \sin(\theta) = 0.8333 \]
Now, use the inverse sine function on a calculator to find the angle θ:
\[ \theta ≈ \sin^{-1}(0.8333) \]
This will give you the approximate value of the angle.
### Solution Steps
1. Identify the triangle sides and the hypotenuse.
2. Apply the sine formula.
3. Utilize the inverse sine function to find θ.
By following these steps, we find that the angle θ is approximately 56.4°.
### Conclusion
Thus, the wire meets the ground at approximately an angle of **56.4°**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2Fda246dc8-f964-460d-bcba-1fe30bf16b4b%2Fd3q9ofb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.
**Question:** At approximately what angle does the wire meet the ground?
### Answer Options
- 33.6°
- 39.8°
- 50.2°
- 56.4°
### Explanation
Consider a right triangle formed with:
- the tree as the vertical side (opposite side) measuring 10 feet,
- the ground as the horizontal side (adjacent side), and
- the wire as the hypotenuse measuring 12 feet.
To find the angle θ at which the wire meets the ground, use the trigonometric relationship: sine (sin).
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
\[ \sin(\theta) = \frac{10}{12} \]
First, find the sine value:
\[ \sin(\theta) = 0.8333 \]
Now, use the inverse sine function on a calculator to find the angle θ:
\[ \theta ≈ \sin^{-1}(0.8333) \]
This will give you the approximate value of the angle.
### Solution Steps
1. Identify the triangle sides and the hypotenuse.
2. Apply the sine formula.
3. Utilize the inverse sine function to find θ.
By following these steps, we find that the angle θ is approximately 56.4°.
### Conclusion
Thus, the wire meets the ground at approximately an angle of **56.4°**.
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