Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Find the measure of side a in a right triangle**
Consider the right triangle \( \triangle ABC \), where:
- \( AB \) is the hypotenuse, \( c = 28 \) meters.
- \( \angle BAC \) is \( 37^\circ \).
- \( \angle ACB \) is the right angle.
- The length of side \( a \) is to be determined.
Using trigonometric principles:
\[ \sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}} \]
Here, \( \theta = 37^\circ \). Thus:
\[ \sin(37^\circ) = \frac{a}{28} \]
Calculating for \( a \):
\[ a = 28 \times \sin(37^\circ) \]
Use a calculator or trigonometric table to find \( \sin(37^\circ) \approx 0.6018 \):
\[ a \approx 28 \times 0.6018 \]
\[ a \approx 16.85 \]
Rounded to the nearest whole number:
\[ a \approx 17 \]
Therefore, the length of side \( a \) is approximately \( 17 \) meters. Please enter the answer in the blank provided below:
\[ a = \_\_\_ \text{ m} \]
\( (Round \ the \ answer \ to \ the \ nearest \ whole \ number.) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F959a643c-45ff-4cba-bf81-f285af0e5e62%2F45c01c44-fae7-4232-9289-3bb69195e749%2Fpre2f9i_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the measure of side a in a right triangle**
Consider the right triangle \( \triangle ABC \), where:
- \( AB \) is the hypotenuse, \( c = 28 \) meters.
- \( \angle BAC \) is \( 37^\circ \).
- \( \angle ACB \) is the right angle.
- The length of side \( a \) is to be determined.
Using trigonometric principles:
\[ \sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}} \]
Here, \( \theta = 37^\circ \). Thus:
\[ \sin(37^\circ) = \frac{a}{28} \]
Calculating for \( a \):
\[ a = 28 \times \sin(37^\circ) \]
Use a calculator or trigonometric table to find \( \sin(37^\circ) \approx 0.6018 \):
\[ a \approx 28 \times 0.6018 \]
\[ a \approx 16.85 \]
Rounded to the nearest whole number:
\[ a \approx 17 \]
Therefore, the length of side \( a \) is approximately \( 17 \) meters. Please enter the answer in the blank provided below:
\[ a = \_\_\_ \text{ m} \]
\( (Round \ the \ answer \ to \ the \ nearest \ whole \ number.) \)
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