Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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![**Problem:**
Solve for \( x \). Round to the nearest tenth, if necessary.
**Diagram Explanation:**
The image contains a right-angled triangle labeled \( \triangle KLM \). The right angle is at vertex \( L \). The side \( KL \) is adjacent to the given angle, \( \angle KML \), which measures 27 degrees.
- **Angle \( \angle KML \) = 27°**
- **Side \( KL \) = 6.3 units**
- **Hypotenuse \( KM \) = \( x \) units (unknown to be solved for)**
**Solution:**
To find the length of the hypotenuse \( x \), we use the cosine trigonometric ratio, since we have the adjacent side and need to find the hypotenuse.
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
Substitute the values:
\[
\cos(27^\circ) = \frac{6.3}{x}
\]
This can be rearranged to solve for \( x \):
\[
x = \frac{6.3}{\cos(27^\circ)}
\]
Using a calculator to find the cosine of 27 degrees:
\[
\cos(27^\circ) \approx 0.8910
\]
Thus,
\[
x = \frac{6.3}{0.8910} \approx 7.1
\]
So, the length of \( x \), rounded to the nearest tenth, is approximately \( 7.1 \text{ units} \).](https://content.bartleby.com/qna-images/question/16ab444c-cc67-4b2e-a5c5-3a02b2df29f8/d392b4e6-76bb-4757-b6ad-46798ed813dd/mfu6kt_processed.jpeg)
Transcribed Image Text:**Problem:**
Solve for \( x \). Round to the nearest tenth, if necessary.
**Diagram Explanation:**
The image contains a right-angled triangle labeled \( \triangle KLM \). The right angle is at vertex \( L \). The side \( KL \) is adjacent to the given angle, \( \angle KML \), which measures 27 degrees.
- **Angle \( \angle KML \) = 27°**
- **Side \( KL \) = 6.3 units**
- **Hypotenuse \( KM \) = \( x \) units (unknown to be solved for)**
**Solution:**
To find the length of the hypotenuse \( x \), we use the cosine trigonometric ratio, since we have the adjacent side and need to find the hypotenuse.
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
Substitute the values:
\[
\cos(27^\circ) = \frac{6.3}{x}
\]
This can be rearranged to solve for \( x \):
\[
x = \frac{6.3}{\cos(27^\circ)}
\]
Using a calculator to find the cosine of 27 degrees:
\[
\cos(27^\circ) \approx 0.8910
\]
Thus,
\[
x = \frac{6.3}{0.8910} \approx 7.1
\]
So, the length of \( x \), rounded to the nearest tenth, is approximately \( 7.1 \text{ units} \).
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