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e length of the hypotenuse. Round to the nearest meter... 52⁰ 201 15 m 24 m D. 10 m 13

e length of the hypotenuse. Round to the nearest meter... 52⁰ 201 15 m 24 m D. 10 m 13

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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### Triangles and Trigonometry: Finding the Length of the Hypotenuse **Problem Statement:** Use the figure below to find the length of the hypotenuse. Round to the nearest meter. --- **Figure Description:** The figure provided is a right-angle triangle with one of the angles labeled as \(52^\circ\). The side adjacent to this angle (base) is labeled as **15 m**. **Multiple-Choice Answers:** A. 19 m B. 0.05 m C. (not visible) D. 10 m --- **Solution Explanation:** To find the hypotenuse (\(c\)) of a right-angle triangle given an angle (\(\theta\)) and the length of the adjacent side (\(a\)), we use the trigonometric function cosine: \[ \cos(\theta) = \frac{a}{c} \] Given: - \( \theta = 52^\circ \) - \( a = 15 m \) Rearranging the formula to solve for \(c\): \[ c = \frac{a}{\cos(\theta)} \] Plugging in the known values: \[ c = \frac{15}{\cos(52^\circ)} \] Using a calculator to find \(\cos(52^\circ) \approx 0.6157\): \[ c \approx \frac{15}{0.6157} \approx 24.4 \] Rounded to the nearest meter, \( c \approx 24 \) meters. Thus, the correct answer is: **C. 24 m**
Transcribed Image Text:### Triangles and Trigonometry: Finding the Length of the Hypotenuse **Problem Statement:** Use the figure below to find the length of the hypotenuse. Round to the nearest meter. --- **Figure Description:** The figure provided is a right-angle triangle with one of the angles labeled as \(52^\circ\). The side adjacent to this angle (base) is labeled as **15 m**. **Multiple-Choice Answers:** A. 19 m B. 0.05 m C. (not visible) D. 10 m --- **Solution Explanation:** To find the hypotenuse (\(c\)) of a right-angle triangle given an angle (\(\theta\)) and the length of the adjacent side (\(a\)), we use the trigonometric function cosine: \[ \cos(\theta) = \frac{a}{c} \] Given: - \( \theta = 52^\circ \) - \( a = 15 m \) Rearranging the formula to solve for \(c\): \[ c = \frac{a}{\cos(\theta)} \] Plugging in the known values: \[ c = \frac{15}{\cos(52^\circ)} \] Using a calculator to find \(\cos(52^\circ) \approx 0.6157\): \[ c \approx \frac{15}{0.6157} \approx 24.4 \] Rounded to the nearest meter, \( c \approx 24 \) meters. Thus, the correct answer is: **C. 24 m**
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