Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter1: Variables, Expressions, And Integers
Section1.8: The Coordinate Plane
Problem 5C
Related questions
Question
![### Problem Statement
**Solve for \( x \) in the triangle. Round your answer to the nearest tenth.**
### Diagram Explanation
The image features a right-angled triangle with one of the angles marked as \(52^\circ\). The hypotenuse of the triangle is labeled as 15 units. The side opposite the \(52^\circ\) angle is labeled as \( x \).
#### Triangle Details:
- **Given:**
- Hypotenuse (\(c\)) = 15 units
- Angle = \(52^\circ\)
- **Find:**
- Opposite side (\(x\))
### Solution Steps:
1. **Use the sine function for the given angle:**
\[
\sin(52^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{x}{15}
\]
2. **Solve for \( x \):**
\[
x = 15 \times \sin(52^\circ)
\]
3. **Calculate \( x \) using a calculator:**
1. Find \(\sin(52^\circ)\):
\[
\sin(52^\circ) \approx 0.7880
\]
2. Multiply by 15:
\[
x \approx 15 \times 0.7880 \approx 11.8
\]
4. **Round to the nearest tenth:**
\[
x \approx 11.8
\]
### Interactive Component
There is a text box to input the calculated value of \( x \), and buttons for submitting the answer, resetting the attempt, and getting hints or help.
- **Input Box:** Where \( x = \_\_\_ \) is to be filled.
- **Buttons:**
- **Check Button (✓)**
- **Reset Button (⟲)**
- **Help Button (?)**
Use these tools to verify if your computed answer is correct and to reset attempts or seek guidance as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd1ff857-92ff-4e51-81f6-c8581968700f%2F904f2ea4-e436-4468-9171-eb89844ce1d6%2Fuvrj8nv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**Solve for \( x \) in the triangle. Round your answer to the nearest tenth.**
### Diagram Explanation
The image features a right-angled triangle with one of the angles marked as \(52^\circ\). The hypotenuse of the triangle is labeled as 15 units. The side opposite the \(52^\circ\) angle is labeled as \( x \).
#### Triangle Details:
- **Given:**
- Hypotenuse (\(c\)) = 15 units
- Angle = \(52^\circ\)
- **Find:**
- Opposite side (\(x\))
### Solution Steps:
1. **Use the sine function for the given angle:**
\[
\sin(52^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{x}{15}
\]
2. **Solve for \( x \):**
\[
x = 15 \times \sin(52^\circ)
\]
3. **Calculate \( x \) using a calculator:**
1. Find \(\sin(52^\circ)\):
\[
\sin(52^\circ) \approx 0.7880
\]
2. Multiply by 15:
\[
x \approx 15 \times 0.7880 \approx 11.8
\]
4. **Round to the nearest tenth:**
\[
x \approx 11.8
\]
### Interactive Component
There is a text box to input the calculated value of \( x \), and buttons for submitting the answer, resetting the attempt, and getting hints or help.
- **Input Box:** Where \( x = \_\_\_ \) is to be filled.
- **Buttons:**
- **Check Button (✓)**
- **Reset Button (⟲)**
- **Help Button (?)**
Use these tools to verify if your computed answer is correct and to reset attempts or seek guidance as needed.
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