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
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![**Trigonometric Angle Calculation Exercise**
**Objective: Solve for \( x \). Round to the nearest tenth of a degree, if necessary.**
The given problem presents a right triangle \( \triangle KLM \) with the following dimensions:
- The hypotenuse \( KM \) measures 6.5 units.
- The adjacent side \( LM \) measures 4.4 units.
- Angle \( x^\circ \) is located at vertex \( M \).
**Diagram Explanation:**
- The right triangle has a right angle at vertex \( L \).
- The hypotenuse \( KM \) is the longest side of the triangle.
- The adjacent side to angle \( x \) is \( LM \).
- The value of the angle \( x \) at vertex \( M \) needs to be calculated.
**Procedure to Find \( x \):**
1. Use the trigonometric function cosine, as it relates the adjacent side and the hypotenuse in a right triangle.
2. The cosine formula is:
\[
\cos{x} = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]
3. Substitute the given values into the formula:
\[
\cos{x} = \frac{LM}{KM} = \frac{4.4}{6.5}
\]
4. Calculate the value of \( \frac{4.4}{6.5} \):
\[
\cos{x} \approx 0.676923
\]
5. Use the inverse cosine function to find \( x \):
\[
x = \cos^{-1}(0.676923)
\]
6. Determine \( x \) using a calculator or appropriate software and round to the nearest tenth of a degree:
\[
x \approx 47.2^\circ
\]
**Answer Field:**
\[ \text{Answer: } x = 47.2^\circ \]
Finally, students should use the provided input box to enter their calculated value and then select "Submit Answer" to verify their solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3bb1cdcc-d635-4109-899e-c60428d000d1%2F3c001442-0a6e-41d0-8bf7-c89921b891ec%2Fdndm50g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Trigonometric Angle Calculation Exercise**
**Objective: Solve for \( x \). Round to the nearest tenth of a degree, if necessary.**
The given problem presents a right triangle \( \triangle KLM \) with the following dimensions:
- The hypotenuse \( KM \) measures 6.5 units.
- The adjacent side \( LM \) measures 4.4 units.
- Angle \( x^\circ \) is located at vertex \( M \).
**Diagram Explanation:**
- The right triangle has a right angle at vertex \( L \).
- The hypotenuse \( KM \) is the longest side of the triangle.
- The adjacent side to angle \( x \) is \( LM \).
- The value of the angle \( x \) at vertex \( M \) needs to be calculated.
**Procedure to Find \( x \):**
1. Use the trigonometric function cosine, as it relates the adjacent side and the hypotenuse in a right triangle.
2. The cosine formula is:
\[
\cos{x} = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]
3. Substitute the given values into the formula:
\[
\cos{x} = \frac{LM}{KM} = \frac{4.4}{6.5}
\]
4. Calculate the value of \( \frac{4.4}{6.5} \):
\[
\cos{x} \approx 0.676923
\]
5. Use the inverse cosine function to find \( x \):
\[
x = \cos^{-1}(0.676923)
\]
6. Determine \( x \) using a calculator or appropriate software and round to the nearest tenth of a degree:
\[
x \approx 47.2^\circ
\]
**Answer Field:**
\[ \text{Answer: } x = 47.2^\circ \]
Finally, students should use the provided input box to enter their calculated value and then select "Submit Answer" to verify their solution.
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