Find a in degrees. 58 3 7 [?]°
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![The image shows a right-angled triangle with sides labeled 3, 7, and \(\sqrt{58}\). The angle opposite the side of length 7 is denoted as \(\alpha\). The task is to find the measure of angle \(\alpha\) in degrees, rounding to the nearest tenth.
### Triangle Description:
- The side of length 3 is adjacent to \(\alpha\).
- The side of length 7 is opposite \(\alpha\).
- The hypotenuse is \(\sqrt{58}\).
### Instructions:
To find angle \(\alpha\), use the trigonometric function tangent, which is the ratio of the opposite side to the adjacent side:
\[
\tan(\alpha) = \frac{7}{3}
\]
To find \(\alpha\), you calculate:
\[
\alpha = \tan^{-1}\left(\frac{7}{3}\right)
\]
Finally, round the answer to the nearest tenth of a degree.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f2c9438-5a89-4288-b691-8fe1dc913be9%2F8dd034b1-658d-41b8-a464-0040d712b2fb%2Fgmjwmdj_processed.png&w=3840&q=75)
Transcribed Image Text:The image shows a right-angled triangle with sides labeled 3, 7, and \(\sqrt{58}\). The angle opposite the side of length 7 is denoted as \(\alpha\). The task is to find the measure of angle \(\alpha\) in degrees, rounding to the nearest tenth.
### Triangle Description:
- The side of length 3 is adjacent to \(\alpha\).
- The side of length 7 is opposite \(\alpha\).
- The hypotenuse is \(\sqrt{58}\).
### Instructions:
To find angle \(\alpha\), use the trigonometric function tangent, which is the ratio of the opposite side to the adjacent side:
\[
\tan(\alpha) = \frac{7}{3}
\]
To find \(\alpha\), you calculate:
\[
\alpha = \tan^{-1}\left(\frac{7}{3}\right)
\]
Finally, round the answer to the nearest tenth of a degree.
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