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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19
![### Geometric and Coordinate Transformations
**Question 19: Find the value of x.**
A diagram is provided containing a circle. Outside the circle, there is a tangent line creating an angle with a point on the circle, resulting in a designated angle of 284°. The question asks to find the value of \( x \).
**Options:**
- A. 142
- B. 76
- C. 208
- D. 104
(Here, you would typically explain the diagram in more detail if available. In this case, the main focus is the given angle and the possible values of \( x \).)
**Question 20: Convert (2, 50°) to rectangular coordinates.**
A polar coordinate (2, 50°) is given. The question asks for its conversion to rectangular coordinates.
**Options:**
- A. (1.5, 1.3)
- B. (−1.3, 1.5)
- C. (1.3, 1.5)
- D. (1.5, −1.3)
**Explanation of Graphs and Diagrams:**
**Diagram for Question 19**
- The diagram shows a circle with a line tangent to it. The angle between this tangent line and another line, extending from the center of the circle to the tangent point, measures 284°. This implies that you may need to consider properties of circle angles and tangent-secant relationships to solve for \( x \).
**Polar to Rectangular Conversion (Question 20)**
- The conversion of polar coordinates \((r,\theta)\) to rectangular coordinates \((x,y)\) is done using the formulas:
\[
x = r \cos(\theta)
\]
\[
y = r \sin(\theta)
\]
Given \( r = 2 \) and \( \theta = 50° \).
### Additional Explanation:
For Question 19:
- Recognize properties of circle angles and tangent lines. The full circle is 360°, making the remaining angle \( 360° - 284° = 76° \). Depending on additional context from geometry principles, this could help find \( x \).
For Question 20:
- Transform the polar coordinates (2, 50°) using the provided formulas:
\[
x = 2 \cos(50°)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d544791-a77c-4b5e-888b-2e8a4014205c%2F0f19b819-df60-41cd-853b-92452550c74d%2Fudhluc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometric and Coordinate Transformations
**Question 19: Find the value of x.**
A diagram is provided containing a circle. Outside the circle, there is a tangent line creating an angle with a point on the circle, resulting in a designated angle of 284°. The question asks to find the value of \( x \).
**Options:**
- A. 142
- B. 76
- C. 208
- D. 104
(Here, you would typically explain the diagram in more detail if available. In this case, the main focus is the given angle and the possible values of \( x \).)
**Question 20: Convert (2, 50°) to rectangular coordinates.**
A polar coordinate (2, 50°) is given. The question asks for its conversion to rectangular coordinates.
**Options:**
- A. (1.5, 1.3)
- B. (−1.3, 1.5)
- C. (1.3, 1.5)
- D. (1.5, −1.3)
**Explanation of Graphs and Diagrams:**
**Diagram for Question 19**
- The diagram shows a circle with a line tangent to it. The angle between this tangent line and another line, extending from the center of the circle to the tangent point, measures 284°. This implies that you may need to consider properties of circle angles and tangent-secant relationships to solve for \( x \).
**Polar to Rectangular Conversion (Question 20)**
- The conversion of polar coordinates \((r,\theta)\) to rectangular coordinates \((x,y)\) is done using the formulas:
\[
x = r \cos(\theta)
\]
\[
y = r \sin(\theta)
\]
Given \( r = 2 \) and \( \theta = 50° \).
### Additional Explanation:
For Question 19:
- Recognize properties of circle angles and tangent lines. The full circle is 360°, making the remaining angle \( 360° - 284° = 76° \). Depending on additional context from geometry principles, this could help find \( x \).
For Question 20:
- Transform the polar coordinates (2, 50°) using the provided formulas:
\[
x = 2 \cos(50°)
\]
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