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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![**Problem 13:** If \( JH = 21 \, \text{in} \), find the length of \( KJG \).
**Diagram Explanation:**
A circle is divided into segments from the center point \( L \). The circle is segmented into the following pieces:
- Arc \( KG \) with central angle of \( 59^\circ \).
- Arc \( JI \) with central angle of \( 85^\circ \).
Other points on the circle are labeled \( K, G, H, J, \) and \( I \).
To solve for the length of \( KJG \), note:
1. \( KJG \) refers to the arc starting at \( K \), passing through \( J \), and ending at \( G \).
2. You need to determine the total angle \( \angle KLG \) by considering complementary angles that sum up to \( 360^\circ \).
Using this information, calculate the arc length using the appropriate formulas or relationships from geometry involving the proportion of \( 360^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46e25c80-76d1-40fc-b8ee-938f2c7ceeae%2F0d3c4f1c-a34e-4cb2-93ec-8d5a876e7981%2Fi75m4wo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 13:** If \( JH = 21 \, \text{in} \), find the length of \( KJG \).
**Diagram Explanation:**
A circle is divided into segments from the center point \( L \). The circle is segmented into the following pieces:
- Arc \( KG \) with central angle of \( 59^\circ \).
- Arc \( JI \) with central angle of \( 85^\circ \).
Other points on the circle are labeled \( K, G, H, J, \) and \( I \).
To solve for the length of \( KJG \), note:
1. \( KJG \) refers to the arc starting at \( K \), passing through \( J \), and ending at \( G \).
2. You need to determine the total angle \( \angle KLG \) by considering complementary angles that sum up to \( 360^\circ \).
Using this information, calculate the arc length using the appropriate formulas or relationships from geometry involving the proportion of \( 360^\circ \).
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