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
how would you do 20? would you use the law of cosines?
![### Solving Similar Triangles
**Problem Statement:**
Solve for \( x \). The triangles in each pair are similar.
#### Question 20:
Given the similar triangles \( \triangle JKL \sim \triangle ABC \):
**Triangle \( \triangle JKL \):**
- Angle \( J \): 58°
- \( \overline{LJ} \): 56 (Length of side between points L and J)
- \( \overline{JK} \): \( 3x - 12 \) (Length of side between points J and K)
**Triangle \( \triangle ABC \):**
- Angle \( B \): 58°
- \( \overline{AB} \): 3 (Length of side between points A and B)
- \( \overline{BC} \): 7 (Length of side between points B and C)
**Options:**
- A) 12
- B) 11
- C) 7
- D) 13
**Diagram Explanation:**
1. The problem contains diagrams of two triangles, \( \triangle JKL \) and \( \triangle ABC \), which are stated to be similar.
2. For \( \triangle JKL \):
- The side \( \overline{LJ} \) is labeled with a length of 56.
- Angle \( J \) is given as 58°.
- The side \( \overline{JK} \) is labeled with an expression \( 3x - 12 \).
3. For \( \triangle ABC \):
- The side \( \overline{AB} \) is labeled with a length of 3.
- Angle \( B \) is given as 58°.
- The side \( \overline{BC} \) is labeled with a length of 7.
Since the triangles are similar, the corresponding sides are proportional. This problem asks you to find the value of \( x \) using this property.
**How to Solve:**
1. Set up the ratio of the corresponding sides since the triangles are similar:
\[
\frac{\overline{LJ}}{\overline{AB}} = \frac{\overline{JK}}{\overline{BC}}
\]
2. Substitute the known values into the proportion:
\[
\frac{56}{3} = \frac{3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c3597d8-30c2-4840-bf6e-c951942ae65e%2F7ea3c77e-5b16-422d-957b-f188b6967514%2F0kr40fe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Similar Triangles
**Problem Statement:**
Solve for \( x \). The triangles in each pair are similar.
#### Question 20:
Given the similar triangles \( \triangle JKL \sim \triangle ABC \):
**Triangle \( \triangle JKL \):**
- Angle \( J \): 58°
- \( \overline{LJ} \): 56 (Length of side between points L and J)
- \( \overline{JK} \): \( 3x - 12 \) (Length of side between points J and K)
**Triangle \( \triangle ABC \):**
- Angle \( B \): 58°
- \( \overline{AB} \): 3 (Length of side between points A and B)
- \( \overline{BC} \): 7 (Length of side between points B and C)
**Options:**
- A) 12
- B) 11
- C) 7
- D) 13
**Diagram Explanation:**
1. The problem contains diagrams of two triangles, \( \triangle JKL \) and \( \triangle ABC \), which are stated to be similar.
2. For \( \triangle JKL \):
- The side \( \overline{LJ} \) is labeled with a length of 56.
- Angle \( J \) is given as 58°.
- The side \( \overline{JK} \) is labeled with an expression \( 3x - 12 \).
3. For \( \triangle ABC \):
- The side \( \overline{AB} \) is labeled with a length of 3.
- Angle \( B \) is given as 58°.
- The side \( \overline{BC} \) is labeled with a length of 7.
Since the triangles are similar, the corresponding sides are proportional. This problem asks you to find the value of \( x \) using this property.
**How to Solve:**
1. Set up the ratio of the corresponding sides since the triangles are similar:
\[
\frac{\overline{LJ}}{\overline{AB}} = \frac{\overline{JK}}{\overline{BC}}
\]
2. Substitute the known values into the proportion:
\[
\frac{56}{3} = \frac{3
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