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P H 1540 M X 380 K

P H 1540 M X 380 K

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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### Right Triangle LKM The image depicts a right triangle labeled ΔLKM. - **Vertices**: The vertices of the triangle are labeled \(L\), \(K\), and \(M\). - **Angles**: - \(\angle LKM\) is a 58° angle. - \(\angle KML\) is a right angle (90°). - \(\angle L\) measures 54°. By calculating the angles in a triangle and using the property that the sum of the angles equals 180°, this helps to verify all angles: \[ \angle KLM = 180° - (\angle LKM + \angle KML) = 180° - (58° + 90°) = 32°. \] - **Sides**: - The horizontal side between L and M is labeled as \(m\). - The hypotenuse between K and M is not labeled with a length. - A vertical side between L and K is labeled \(x\). This example layout can be used to demonstrate solving problems involving right triangles, using trigonometric identities or the Pythagorean theorem. **Task**: Solve the right triangle ΔLKM using the given angle measurements. Be sure to use the trigonometric identities: - \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\) - \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\) - \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\) Let's label the sides for reference: - Opposite to \(\angle KLM (32°)\) is \(LK\). - Adjacent to \(\angle KLM (32°)\) and opposite to \(\angle LKM (58°)\) is \(LM\). - Hypotenuse is \(KM\).
Transcribed Image Text:### Right Triangle LKM The image depicts a right triangle labeled ΔLKM. - **Vertices**: The vertices of the triangle are labeled \(L\), \(K\), and \(M\). - **Angles**: - \(\angle LKM\) is a 58° angle. - \(\angle KML\) is a right angle (90°). - \(\angle L\) measures 54°. By calculating the angles in a triangle and using the property that the sum of the angles equals 180°, this helps to verify all angles: \[ \angle KLM = 180° - (\angle LKM + \angle KML) = 180° - (58° + 90°) = 32°. \] - **Sides**: - The horizontal side between L and M is labeled as \(m\). - The hypotenuse between K and M is not labeled with a length. - A vertical side between L and K is labeled \(x\). This example layout can be used to demonstrate solving problems involving right triangles, using trigonometric identities or the Pythagorean theorem. **Task**: Solve the right triangle ΔLKM using the given angle measurements. Be sure to use the trigonometric identities: - \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\) - \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\) - \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\) Let's label the sides for reference: - Opposite to \(\angle KLM (32°)\) is \(LK\). - Adjacent to \(\angle KLM (32°)\) and opposite to \(\angle LKM (58°)\) is \(LM\). - Hypotenuse is \(KM\).
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