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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Can you please answer these clearly ? Thanks !
Transcribed Image Text:The image depicts a trigonometry problem where you need to find the length of the side labeled "x" in a right triangle. The diagram shows:
- A right triangle with a horizontal line parallel to the ground.
- An angle of 22° at the top of the triangle.
- The vertical line opposite the 22° angle is labeled "x."
- The bottom of the diagram includes "x = _________" with an empty box indicating where the solution should be placed.
Students are required to use trigonometric ratios, most likely tangent, to solve for the unknown side "x" given the angle. The problem encourages the application of trigonometry to solve real-world height problems.
![Here's a transcription and explanation of the diagram:
**Diagram Description:**
The diagram consists of three intersecting lines forming various angles. There are angles marked as \(55^\circ\), \(x^\circ\), and \(y^\circ\). The angles are positioned as follows:
1. \(55^\circ\) is an angle formed between a horizontal line and a diagonal line.
2. \(x^\circ\) is placed as the vertically opposite angle to \(55^\circ\), sharing the vertex with it.
3. \(y^\circ\) is adjacent to the \(55^\circ\) angle on the opposite side of the transversal line.
**Objective:**
The goal is to find the values of \(x\) and \(y\).
**Equations:**
- Vertically opposite angles are equal, so \(x = 55^\circ\).
- Since \(y\) and \(55^\circ\) form a linear pair (sum to \(180^\circ\)), you can use the equation:
\[
y + 55^\circ = 180^\circ
\]
\[
y = 180^\circ - 55^\circ
\]
\[
y = 125^\circ
\]
**Blank Spaces for Solutions:**
```
X = ___________
Y = ___________
```
To fill these in, we have:
```
X = 55
Y = 125
```](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9dfbebbf-8e50-4299-b8dd-04968c79c6a1%2Fea6f0027-8d4f-4559-a946-f0eb4eaaa647%2Fpbpcklc_processed.png&w=3840&q=75)
Transcribed Image Text:Here's a transcription and explanation of the diagram:
**Diagram Description:**
The diagram consists of three intersecting lines forming various angles. There are angles marked as \(55^\circ\), \(x^\circ\), and \(y^\circ\). The angles are positioned as follows:
1. \(55^\circ\) is an angle formed between a horizontal line and a diagonal line.
2. \(x^\circ\) is placed as the vertically opposite angle to \(55^\circ\), sharing the vertex with it.
3. \(y^\circ\) is adjacent to the \(55^\circ\) angle on the opposite side of the transversal line.
**Objective:**
The goal is to find the values of \(x\) and \(y\).
**Equations:**
- Vertically opposite angles are equal, so \(x = 55^\circ\).
- Since \(y\) and \(55^\circ\) form a linear pair (sum to \(180^\circ\)), you can use the equation:
\[
y + 55^\circ = 180^\circ
\]
\[
y = 180^\circ - 55^\circ
\]
\[
y = 125^\circ
\]
**Blank Spaces for Solutions:**
```
X = ___________
Y = ___________
```
To fill these in, we have:
```
X = 55
Y = 125
```
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