Find X rounded to one decimal
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
Find X rounded to one decimal
Transcribed Image Text:The image depicts a right triangle. The triangle has a 30-degree angle and a right angle. One side, opposite the 30-degree angle, is labeled with a length of 2. The hypotenuse is not labeled with a numerical value but is denoted with the variable 'x'.
To solve for 'x', use the properties of a 30-60-90 triangle:
- The side opposite the 30-degree angle is half the hypotenuse.
- Therefore, if the side opposite the 30-degree angle is 2, then the hypotenuse, 'x', is 4.
Thus, \( x = 4 \).
![**Problem:**
Find \( x \) rounded to one decimal place.
**Diagram Description:**
The image shows a right triangle with:
- An angle of \( 30^\circ \).
- The side opposite the \( 30^\circ \) angle is labeled \( 2 \).
- The adjacent side to the \( 30^\circ \) angle is labeled \( x \).
**Solution Steps:**
1. **Identify the Appropriate Trigonometric Function:**
Since we have the opposite side and need to find the adjacent side, use the tangent function:
\[
\tan(30^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2}{x}
\]
2. **Solve for \( x \):**
\[
x = \frac{2}{\tan(30^\circ)}
\]
3. **Calculate \( \tan(30^\circ) \):**
\(\tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.577\)
4. **Find \( x \):**
\[
x = \frac{2}{0.577} \approx 3.5
\]
5. **Conclusion:**
\( x \) rounded to one decimal place is approximately \( 3.5 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e9cf07e-9961-4494-a89d-ab64214ea034%2F64594703-d01d-4dda-9eef-2a417ec764e8%2Fbt0scio.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Find \( x \) rounded to one decimal place.
**Diagram Description:**
The image shows a right triangle with:
- An angle of \( 30^\circ \).
- The side opposite the \( 30^\circ \) angle is labeled \( 2 \).
- The adjacent side to the \( 30^\circ \) angle is labeled \( x \).
**Solution Steps:**
1. **Identify the Appropriate Trigonometric Function:**
Since we have the opposite side and need to find the adjacent side, use the tangent function:
\[
\tan(30^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2}{x}
\]
2. **Solve for \( x \):**
\[
x = \frac{2}{\tan(30^\circ)}
\]
3. **Calculate \( \tan(30^\circ) \):**
\(\tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.577\)
4. **Find \( x \):**
\[
x = \frac{2}{0.577} \approx 3.5
\]
5. **Conclusion:**
\( x \) rounded to one decimal place is approximately \( 3.5 \).
Expert Solution
Step 1
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning