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3. What is the tangent ratio of angle KJL? K 48 30° 30°

3. What is the tangent ratio of angle KJL? K 48 30° 30°

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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### Problem Statement **Question 3: What is the tangent ratio of angle KJL?** ### Diagram Description The diagram depicts an isosceles triangle \(JKL\) with \(J\) and \(K\) as the endpoints of the equal sides, and \(L\) as the opposite vertex. The triangle is divided into two right triangles by line \(ML\), where \(M\) is the midpoint of \(JK\). - \( \angle JLM = 30^\circ\) - \( \angle KLM = 30^\circ\) - The length \(JK = 48\) - \(ML\) is perpendicular to \(JK\), hence \( \angle JML\) and \( \angle KML\) are right angles (\(90^\circ\)). ### Answer Choices 1. \( \frac{24}{48} \) 2. \( \frac{48 \sqrt{3}}{48} \) 3. \( \frac{24 \sqrt{3}}{48} \) ### Explanation To solve for the tangent of \( \angle KJL\): 1. Identify the right triangle, \( \triangle JML\). 2. Use \( \angle JLM = 30^\circ \) to find \( \tan(30^\circ) \). 3. Apply the formula \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \) where \( \theta=30^\circ \). For \( \angle JLM = 30^\circ \): - Opposite side to \( \angle JLM \): \( ML \) - Adjacent side to \( \angle JLM \): \( JM \) Since \(JK = 48\) and \(M\) is the midpoint (\( JM = MK = \frac{48}{2} = 24\)): - Tangent of \(30^\circ\) is \( \frac{ML}{JM} = \frac{ML}{24} \) - Note that \( ML = 24 \times \tan(30^\circ)\) Given that \( \tan(30^\circ) = \frac{1}{\sqrt{3}} \), we can simplify: \[ \tan(\angle JLM) = \frac{24 \times \frac{1}{\sqrt{3}}}{24} = \frac{24
Transcribed Image Text:### Problem Statement **Question 3: What is the tangent ratio of angle KJL?** ### Diagram Description The diagram depicts an isosceles triangle \(JKL\) with \(J\) and \(K\) as the endpoints of the equal sides, and \(L\) as the opposite vertex. The triangle is divided into two right triangles by line \(ML\), where \(M\) is the midpoint of \(JK\). - \( \angle JLM = 30^\circ\) - \( \angle KLM = 30^\circ\) - The length \(JK = 48\) - \(ML\) is perpendicular to \(JK\), hence \( \angle JML\) and \( \angle KML\) are right angles (\(90^\circ\)). ### Answer Choices 1. \( \frac{24}{48} \) 2. \( \frac{48 \sqrt{3}}{48} \) 3. \( \frac{24 \sqrt{3}}{48} \) ### Explanation To solve for the tangent of \( \angle KJL\): 1. Identify the right triangle, \( \triangle JML\). 2. Use \( \angle JLM = 30^\circ \) to find \( \tan(30^\circ) \). 3. Apply the formula \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \) where \( \theta=30^\circ \). For \( \angle JLM = 30^\circ \): - Opposite side to \( \angle JLM \): \( ML \) - Adjacent side to \( \angle JLM \): \( JM \) Since \(JK = 48\) and \(M\) is the midpoint (\( JM = MK = \frac{48}{2} = 24\)): - Tangent of \(30^\circ\) is \( \frac{ML}{JM} = \frac{ML}{24} \) - Note that \( ML = 24 \times \tan(30^\circ)\) Given that \( \tan(30^\circ) = \frac{1}{\sqrt{3}} \), we can simplify: \[ \tan(\angle JLM) = \frac{24 \times \frac{1}{\sqrt{3}}}{24} = \frac{24
### Angle and Triangle Ratio Question Below is a diagram and a set of multiple-choice options for a problem involving triangles and angle measurements. #### Diagram Description - The diagram depicts a triangle with a 30°-30°-120° configuration. - Point L is at the vertex of the two 30° angles. - The side opposite the 120° angle is labeled 48. #### Multiple Choice Options Select the correct length of the other sides of the triangle from the options below: 1. \(\frac{24}{48 \sqrt{3}}\) 2. \(\frac{24 \sqrt{3}}{48}\) 3. \(\frac{24 \sqrt{3}}{24}\) 4. \(\frac{24}{24 \sqrt{3}}\) Please refer to the figure and select the correct option that represents the length based on the given angle measures and the side length.
Transcribed Image Text:### Angle and Triangle Ratio Question Below is a diagram and a set of multiple-choice options for a problem involving triangles and angle measurements. #### Diagram Description - The diagram depicts a triangle with a 30°-30°-120° configuration. - Point L is at the vertex of the two 30° angles. - The side opposite the 120° angle is labeled 48. #### Multiple Choice Options Select the correct length of the other sides of the triangle from the options below: 1. \(\frac{24}{48 \sqrt{3}}\) 2. \(\frac{24 \sqrt{3}}{48}\) 3. \(\frac{24 \sqrt{3}}{24}\) 4. \(\frac{24}{24 \sqrt{3}}\) Please refer to the figure and select the correct option that represents the length based on the given angle measures and the side length.
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