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A 44 55 33 In ENABC tan0 = AB BC The angle 4.4 33 teen (214 33 =tcen (+) 53' R 53.

A 44 55 33 In ENABC tan0 = AB BC The angle 4.4 33 teen (214 33 =tcen (+) 53' R 53.

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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can anyone answer why this would be tan and not sin? thanks!
### Expert Answer **Step 1** a) We will solve the problem. **Step 2** b) In the given image, we have a right triangle \( \triangle ABC \). The two legs of the triangle are labeled as 44 and 33, and the hypotenuse is labeled as 55. The image includes the following calculations: 1. \( \tan \theta = \frac{AB}{BC} = \frac{44}{33} \) 2. Simplify the fraction: \( \frac{44}{33} = \frac{4}{3} \) 3. \( \theta = \tan^{-1} \left(\frac{4}{3}\right) \approx 53^\circ \) Thus, the angle \( \theta \) is approximately \( 53^\circ \). **Explanation of Diagram:** The diagram shows a right triangle labeled as \( \triangle ABC \) with the following: - The side opposite to the angle θ (opposite side) is labeled 44. - The adjacent side to the angle θ (adjacent side) is labeled 33. - The hypotenuse (the longest side) is labeled 55. This solution makes use of the tangent function in trigonometry to determine the angle \( \theta \). The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. **Query: Was this solution helpful?** *Yes* *No* --- This transcription ensures the information is clearly presented for educational purposes, detailing the steps taken to solve the problem and explaining the diagram included in the image.
Transcribed Image Text:### Expert Answer **Step 1** a) We will solve the problem. **Step 2** b) In the given image, we have a right triangle \( \triangle ABC \). The two legs of the triangle are labeled as 44 and 33, and the hypotenuse is labeled as 55. The image includes the following calculations: 1. \( \tan \theta = \frac{AB}{BC} = \frac{44}{33} \) 2. Simplify the fraction: \( \frac{44}{33} = \frac{4}{3} \) 3. \( \theta = \tan^{-1} \left(\frac{4}{3}\right) \approx 53^\circ \) Thus, the angle \( \theta \) is approximately \( 53^\circ \). **Explanation of Diagram:** The diagram shows a right triangle labeled as \( \triangle ABC \) with the following: - The side opposite to the angle θ (opposite side) is labeled 44. - The adjacent side to the angle θ (adjacent side) is labeled 33. - The hypotenuse (the longest side) is labeled 55. This solution makes use of the tangent function in trigonometry to determine the angle \( \theta \). The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. **Query: Was this solution helpful?** *Yes* *No* --- This transcription ensures the information is clearly presented for educational purposes, detailing the steps taken to solve the problem and explaining the diagram included in the image.
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