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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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100%
**Steps to Solve:**
1. **Identify the Trigonometric Function:**
- Since we are given the lengths of the opposite side (50) and the hypotenuse (59) relative to angle \( x \), we use the sine function.
\[
\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{50}{59}
\]
2. **Calculate the Angle \( x \):**
- Use the inverse sine function (\(\sin^{-1}\)) to find the angle \( x \).
\[
x = \sin^{-1}\left(\frac{50}{59}\right)
\]
3. **Round the Angle:**
- Calculate the value and round it to the nearest tenth of a degree.
\[
x \approx 59.5^\circ
\]
**Conclusion:**
The value of angle \( x \) is approximately \( 59.5^\circ \) when rounded to the nearest tenth of a degree.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb223a19b-0fd0-443c-881a-6f762159fad5%2F92bec86f-bb8f-42ec-b056-c1732878d7a9%2Fiqbyb3v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving for x: Trigonometry Application
**Problem Statement:**
Solve for \( x \). Round to the nearest tenth of a degree, if necessary.
**Diagram Description:**
The problem includes a right triangle \( \triangle IJH \) with the following lengths:
- The length of side \( JI \) is 50 units.
- The length of side \( JH \) is 59 units.
- \( IJH \) is a right angle, with \( JI \) as one leg, and \( JH \) as the hypotenuse.
The angle \( x \) is located at vertex \( J \), opposite the side \( IJ \).
**Steps to Solve:**
1. **Identify the Trigonometric Function:**
- Since we are given the lengths of the opposite side (50) and the hypotenuse (59) relative to angle \( x \), we use the sine function.
\[
\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{50}{59}
\]
2. **Calculate the Angle \( x \):**
- Use the inverse sine function (\(\sin^{-1}\)) to find the angle \( x \).
\[
x = \sin^{-1}\left(\frac{50}{59}\right)
\]
3. **Round the Angle:**
- Calculate the value and round it to the nearest tenth of a degree.
\[
x \approx 59.5^\circ
\]
**Conclusion:**
The value of angle \( x \) is approximately \( 59.5^\circ \) when rounded to the nearest tenth of a degree.
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