Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter1: The Six Trigonometric Functions
Section: Chapter Questions
Problem 2GP
Related questions
Question
![### Triangles and Trigonometry: Finding the Length of the Hypotenuse
**Problem Statement:**
Use the figure below to find the length of the hypotenuse. Round to the nearest meter.
---
**Figure Description:**
The figure provided is a right-angle triangle with one of the angles labeled as \(52^\circ\). The side adjacent to this angle (base) is labeled as **15 m**.
**Multiple-Choice Answers:**
A. 19 m
B. 0.05 m
C. (not visible)
D. 10 m
---
**Solution Explanation:**
To find the hypotenuse (\(c\)) of a right-angle triangle given an angle (\(\theta\)) and the length of the adjacent side (\(a\)), we use the trigonometric function cosine:
\[ \cos(\theta) = \frac{a}{c} \]
Given:
- \( \theta = 52^\circ \)
- \( a = 15 m \)
Rearranging the formula to solve for \(c\):
\[ c = \frac{a}{\cos(\theta)} \]
Plugging in the known values:
\[ c = \frac{15}{\cos(52^\circ)} \]
Using a calculator to find \(\cos(52^\circ) \approx 0.6157\):
\[ c \approx \frac{15}{0.6157} \approx 24.4 \]
Rounded to the nearest meter, \( c \approx 24 \) meters.
Thus, the correct answer is:
**C. 24 m**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5a061b4-0108-4a51-81fc-44207999c893%2Fca6c1633-22e3-4b44-9c3c-1e3328c59773%2Filnxfub_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Triangles and Trigonometry: Finding the Length of the Hypotenuse
**Problem Statement:**
Use the figure below to find the length of the hypotenuse. Round to the nearest meter.
---
**Figure Description:**
The figure provided is a right-angle triangle with one of the angles labeled as \(52^\circ\). The side adjacent to this angle (base) is labeled as **15 m**.
**Multiple-Choice Answers:**
A. 19 m
B. 0.05 m
C. (not visible)
D. 10 m
---
**Solution Explanation:**
To find the hypotenuse (\(c\)) of a right-angle triangle given an angle (\(\theta\)) and the length of the adjacent side (\(a\)), we use the trigonometric function cosine:
\[ \cos(\theta) = \frac{a}{c} \]
Given:
- \( \theta = 52^\circ \)
- \( a = 15 m \)
Rearranging the formula to solve for \(c\):
\[ c = \frac{a}{\cos(\theta)} \]
Plugging in the known values:
\[ c = \frac{15}{\cos(52^\circ)} \]
Using a calculator to find \(\cos(52^\circ) \approx 0.6157\):
\[ c \approx \frac{15}{0.6157} \approx 24.4 \]
Rounded to the nearest meter, \( c \approx 24 \) meters.
Thus, the correct answer is:
**C. 24 m**
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