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13. If JH = 21 in, find the length of KJG. L 59° 85 H

13. If JH = 21 in, find the length of KJG. L 59° 85 H

Elementary Geometry For College Students, 7e
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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Number 13 please show work
**Problem 11:** - **Task:** If \( NR = 8 \, \text{ft} \), find the length of \( NMP \). - **Diagram Explanation:** The circle is divided into two sections, with central angles labeled as \( 18^\circ \) and \( 162^\circ \). The arc labeled \( NMP \) corresponds to the angle \( 162^\circ \). - **Solution Steps:** 1. Use the formula for arc length: \(\text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r \). 2. Set up the proportion: \(\frac{198}{360} = \frac{x}{2(8)\pi} \). 3. Solve for \( x \): \( 198 \times \frac{16\pi}{360} = x \). **Problem 13:** - **Task:** If \( JH = 21 \, \text{in} \), find the length of \( KJG \). - **Diagram Explanation:** A circle is bisected by diameter \( JH \), creating central angles \( 59^\circ \) and \( 85^\circ \). **Problem 15:** - **Task:** If \( WS = 4.5 \, \text{mm} \), find the length of \( TS \). - **Diagram Explanation:** The circle has been divided into sections with central angles of \( 128^\circ \) and \( 31^\circ \). **General Note:** This exercise involves using proportions to determine arc lengths based on central angles and diameters of circles. It is a practical application of the formula for arc length in circle geometry.
Transcribed Image Text:**Problem 11:** - **Task:** If \( NR = 8 \, \text{ft} \), find the length of \( NMP \). - **Diagram Explanation:** The circle is divided into two sections, with central angles labeled as \( 18^\circ \) and \( 162^\circ \). The arc labeled \( NMP \) corresponds to the angle \( 162^\circ \). - **Solution Steps:** 1. Use the formula for arc length: \(\text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r \). 2. Set up the proportion: \(\frac{198}{360} = \frac{x}{2(8)\pi} \). 3. Solve for \( x \): \( 198 \times \frac{16\pi}{360} = x \). **Problem 13:** - **Task:** If \( JH = 21 \, \text{in} \), find the length of \( KJG \). - **Diagram Explanation:** A circle is bisected by diameter \( JH \), creating central angles \( 59^\circ \) and \( 85^\circ \). **Problem 15:** - **Task:** If \( WS = 4.5 \, \text{mm} \), find the length of \( TS \). - **Diagram Explanation:** The circle has been divided into sections with central angles of \( 128^\circ \) and \( 31^\circ \). **General Note:** This exercise involves using proportions to determine arc lengths based on central angles and diameters of circles. It is a practical application of the formula for arc length in circle geometry.
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