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
Related questions
Question
![### Triangles - Solving for x
**Problem Statement:**
Solve for \( x \) in the triangle. Round your answer to the nearest tenth.
**Given:**
- Right triangle
- One leg is known to be 10 units in length.
- One of the non-right angles is \( 47^\circ \).
**Diagram Description:**
The triangle is right-angled with:
- The vertical leg labeled as 10 units.
- The hypotenuse labeled as \( x \).
- The angle adjacent to the horizontal leg and opposite the hypotenuse marked as \( 47^\circ \).
**Solution Box:**
\( x = \) [Input Box]
**Explanation:**
To find the hypotenuse \( x \) in a right-angled triangle using a known angle and the length of the opposite side, you can use the sine function. The sine of an angle in a right triangle is the ratio of the opposite side to the hypotenuse.
For \( \theta = 47^\circ \):
\[ \sin(47^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here:
\[ \sin(47^\circ) = \frac{10}{x} \]
Solving for \( x \):
\[ x = \frac{10}{\sin(47^\circ)} \]
Use a calculator to solve for \( x \):
\[ x \approx \frac{10}{0.7314} \approx 13.7 \]
So,
\[ x \approx 13.7 \text{ (to the nearest tenth)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd1ff857-92ff-4e51-81f6-c8581968700f%2F49caedf7-0276-4b21-b6dc-57624c8b6ce3%2F3p8nrk4s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Triangles - Solving for x
**Problem Statement:**
Solve for \( x \) in the triangle. Round your answer to the nearest tenth.
**Given:**
- Right triangle
- One leg is known to be 10 units in length.
- One of the non-right angles is \( 47^\circ \).
**Diagram Description:**
The triangle is right-angled with:
- The vertical leg labeled as 10 units.
- The hypotenuse labeled as \( x \).
- The angle adjacent to the horizontal leg and opposite the hypotenuse marked as \( 47^\circ \).
**Solution Box:**
\( x = \) [Input Box]
**Explanation:**
To find the hypotenuse \( x \) in a right-angled triangle using a known angle and the length of the opposite side, you can use the sine function. The sine of an angle in a right triangle is the ratio of the opposite side to the hypotenuse.
For \( \theta = 47^\circ \):
\[ \sin(47^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here:
\[ \sin(47^\circ) = \frac{10}{x} \]
Solving for \( x \):
\[ x = \frac{10}{\sin(47^\circ)} \]
Use a calculator to solve for \( x \):
\[ x \approx \frac{10}{0.7314} \approx 13.7 \]
So,
\[ x \approx 13.7 \text{ (to the nearest tenth)} \]
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