Solve for x. Round to the nearest tenth, if necessary. R 56 S 48°
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°.
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Question
Solve for xx. Round to the nearest tenth, if necessary.
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### Solve for \( x \). Round to the nearest tenth, if necessary.
The diagram provided is a right triangle labeled \( \triangle SRQ \):
- \( \triangle SRQ \) has vertices \( S \), \( R \), \( Q \).
- \(\angle SRQ \) is a right angle (denoted by a small square at \( R \)).
- \(\angle SQR\) measures \( 48^\circ \).
- The side opposite \(\angle SQR\) (denoted as \( RQ \)) measures \( 56 \) units.
- The side \( SQ \) is unknown and denoted as \( x \).
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To solve for \( x \) (the side opposite the angle \( \angle R \)), we can employ trigonometric ratios. Specifically, we can use the tangent function which relates the opposite side to the adjacent side:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Given:
- \(\theta = 48^\circ\)
- \(\text{opposite} = 56\) (side \( RQ \))
- \(\text{adjacent} = x \) (side \( SQ \))
So,
\[ \tan(48^\circ) = \frac{56}{x} \]
Solving for \( x \):
\[ x \cdot \tan(48^\circ) = 56 \]
\[ x = \frac{56}{\tan(48^\circ)} \]
Using a calculator to find \(\tan(48^\circ)\):
\[ \tan(48^\circ) \approx 1.1106 \]
Then,
\[ x \approx \frac{56}{1.1106} \approx 50.4 \]
Thus, the value of \( x \) rounded to the nearest tenth is:
\[ x \approx 50.4 \]
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Transcribed Image Text:---
### Solve for \( x \). Round to the nearest tenth, if necessary.
The diagram provided is a right triangle labeled \( \triangle SRQ \):
- \( \triangle SRQ \) has vertices \( S \), \( R \), \( Q \).
- \(\angle SRQ \) is a right angle (denoted by a small square at \( R \)).
- \(\angle SQR\) measures \( 48^\circ \).
- The side opposite \(\angle SQR\) (denoted as \( RQ \)) measures \( 56 \) units.
- The side \( SQ \) is unknown and denoted as \( x \).
---
To solve for \( x \) (the side opposite the angle \( \angle R \)), we can employ trigonometric ratios. Specifically, we can use the tangent function which relates the opposite side to the adjacent side:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Given:
- \(\theta = 48^\circ\)
- \(\text{opposite} = 56\) (side \( RQ \))
- \(\text{adjacent} = x \) (side \( SQ \))
So,
\[ \tan(48^\circ) = \frac{56}{x} \]
Solving for \( x \):
\[ x \cdot \tan(48^\circ) = 56 \]
\[ x = \frac{56}{\tan(48^\circ)} \]
Using a calculator to find \(\tan(48^\circ)\):
\[ \tan(48^\circ) \approx 1.1106 \]
Then,
\[ x \approx \frac{56}{1.1106} \approx 50.4 \]
Thus, the value of \( x \) rounded to the nearest tenth is:
\[ x \approx 50.4 \]
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