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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![### Solve for x. Round to the nearest tenth, if necessary.
The diagram provided is a right triangle, denoted as triangle \( \Delta WVU \), with the following information:
- Angle \( \angle WUV \) is \( 34^\circ \).
- Segment \( UV \) measures 6.7 units.
- The hypotenuse of the triangle is \( WV \), where segment \( WV = x \), the quantity to be determined.
- Angle \( \angle WVU \) is the right angle (90 degrees), indicated by the small square at vertex V.
#### Explanation for the Diagram
1. **Triangle Configuration:**
- \( \triangle WVU \) is arranged such that point \( V \) is at the right angle.
- Point \( W \) is at the left of point \( V \) on the horizontal base, and point \( U \) is to the right of point \( V \) with an upward diagonal.
2. **Sides and Angles:**
- \( x \): The hypotenuse of the right triangle, extending from point \( W \) to point \( V \).
- 6.7 units: The length of side \( UV \), extending from point \( U \) to point \( V \).
- 34 degrees: The angle \( \angle WUV \), located at point \( U \).
#### Problem Objective
- **Objective:** To calculate the length of the hypotenuse \( x \) using the given angle and the length of one of the triangle's legs.
### Steps to Solve
Using trigonometric relationships in a right triangle involves:
1. **Trigonometric Function:** To find \( x \), use the cosine function because it relates the adjacent side to the hypotenuse:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Here, \( \theta = 34^\circ \), the adjacent side is \( 6.7 \), and the hypotenuse is \( x \).
2. **Equation Setup:**
\[
\cos(34^\circ) = \frac{6.7}{x}
\]
3. **Solving for \( x \):**
\[
x = \frac{6.7}{\cos(34^\circ)}
\]
4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17ee36ea-a061-4aba-8bad-366095b0251b%2F6f36b559-8367-463d-bca9-0ca72d6266f5%2F05xi7t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solve for x. Round to the nearest tenth, if necessary.
The diagram provided is a right triangle, denoted as triangle \( \Delta WVU \), with the following information:
- Angle \( \angle WUV \) is \( 34^\circ \).
- Segment \( UV \) measures 6.7 units.
- The hypotenuse of the triangle is \( WV \), where segment \( WV = x \), the quantity to be determined.
- Angle \( \angle WVU \) is the right angle (90 degrees), indicated by the small square at vertex V.
#### Explanation for the Diagram
1. **Triangle Configuration:**
- \( \triangle WVU \) is arranged such that point \( V \) is at the right angle.
- Point \( W \) is at the left of point \( V \) on the horizontal base, and point \( U \) is to the right of point \( V \) with an upward diagonal.
2. **Sides and Angles:**
- \( x \): The hypotenuse of the right triangle, extending from point \( W \) to point \( V \).
- 6.7 units: The length of side \( UV \), extending from point \( U \) to point \( V \).
- 34 degrees: The angle \( \angle WUV \), located at point \( U \).
#### Problem Objective
- **Objective:** To calculate the length of the hypotenuse \( x \) using the given angle and the length of one of the triangle's legs.
### Steps to Solve
Using trigonometric relationships in a right triangle involves:
1. **Trigonometric Function:** To find \( x \), use the cosine function because it relates the adjacent side to the hypotenuse:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Here, \( \theta = 34^\circ \), the adjacent side is \( 6.7 \), and the hypotenuse is \( x \).
2. **Equation Setup:**
\[
\cos(34^\circ) = \frac{6.7}{x}
\]
3. **Solving for \( x \):**
\[
x = \frac{6.7}{\cos(34^\circ)}
\]
4.
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