Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.9: Direct Variation
Problem 15P
Related questions
Question
![**Problem Statement:**
Find \( x \). Round your answer to the nearest tenth of a degree.
**Diagram:**
The given diagram is a right-angled triangle with the following details:
- The side opposite the angle \( x \) is labeled as 24.
- The side adjacent to the angle \( x \) is labeled as 23.
- The right angle is indicated in the bottom left corner of the triangle.
**Task:**
Calculate the angle \( x \) in degrees and round your answer to the nearest tenth of a degree. Input your answer in the provided box.
**Answer Box:**
\[ x = \boxed{ }^\circ \]
**Solution:**
To find the angle \( x \), you can use the tangent function in trigonometry:
\[ \tan(x) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case:
\[ \tan(x) = \frac{24}{23} \]
Using the inverse tangent function (arctan or \(\tan^{-1}\)) on a calculator, you can find \( x \):
\[ x = \tan^{-1}\left(\frac{24}{23}\right) \]
Compute this value to get the angle \( x \) and then round it to the nearest tenth of a degree.
**Note:**
To perform the computation, ensure your calculator is set to degrees mode. Input the fraction and use the \(\tan^{-1}\) function to find the required angle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14a97047-56a8-420b-97d8-c66168d5d651%2F94e01280-f83f-4f2f-99a6-6f9b9d5c50c9%2Fsweji6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find \( x \). Round your answer to the nearest tenth of a degree.
**Diagram:**
The given diagram is a right-angled triangle with the following details:
- The side opposite the angle \( x \) is labeled as 24.
- The side adjacent to the angle \( x \) is labeled as 23.
- The right angle is indicated in the bottom left corner of the triangle.
**Task:**
Calculate the angle \( x \) in degrees and round your answer to the nearest tenth of a degree. Input your answer in the provided box.
**Answer Box:**
\[ x = \boxed{ }^\circ \]
**Solution:**
To find the angle \( x \), you can use the tangent function in trigonometry:
\[ \tan(x) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case:
\[ \tan(x) = \frac{24}{23} \]
Using the inverse tangent function (arctan or \(\tan^{-1}\)) on a calculator, you can find \( x \):
\[ x = \tan^{-1}\left(\frac{24}{23}\right) \]
Compute this value to get the angle \( x \) and then round it to the nearest tenth of a degree.
**Note:**
To perform the computation, ensure your calculator is set to degrees mode. Input the fraction and use the \(\tan^{-1}\) function to find the required angle.
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