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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### Finding the Length of Side 'a' in a Right Triangle
#### Problem Statement:
Find the measure of side \( a \).
#### Diagram and Given Data:
The provided diagram shows a right triangle \( \triangle ABC \) where:
- \(\angle A = 37^\circ\)
- The hypotenuse \( c = 20 \, \text{m} \)
- The side opposite \(\angle A\) is labeled \( a \)
#### Calculation:
To find the side \( a \), we use the sine function in trigonometry, which relates the angle to the ratio of the opposite side and the hypotenuse in a right-angled triangle:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
\[ \sin(37^\circ) = \frac{a}{20} \]
Solving for \( a \):
\[ a = 20 \times \sin(37^\circ) \]
Using the sine value:
\[ \sin(37^\circ) \approx 0.6018 \]
\[ a = 20 \times 0.6018 \approx 12.036 \]
Therefore:
\[ a \approx 12 \, \text{m} \]
(Note: Round the answer to the nearest whole number.)
---
### Answer:
\( a = \boxed{12} \, \text{m} \)
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F959a643c-45ff-4cba-bf81-f285af0e5e62%2F5ed1d110-c1f4-4df4-82aa-0b7d50d44cb0%2Fkagtuea_processed.png&w=3840&q=75)
Transcribed Image Text:---
### Finding the Length of Side 'a' in a Right Triangle
#### Problem Statement:
Find the measure of side \( a \).
#### Diagram and Given Data:
The provided diagram shows a right triangle \( \triangle ABC \) where:
- \(\angle A = 37^\circ\)
- The hypotenuse \( c = 20 \, \text{m} \)
- The side opposite \(\angle A\) is labeled \( a \)
#### Calculation:
To find the side \( a \), we use the sine function in trigonometry, which relates the angle to the ratio of the opposite side and the hypotenuse in a right-angled triangle:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
\[ \sin(37^\circ) = \frac{a}{20} \]
Solving for \( a \):
\[ a = 20 \times \sin(37^\circ) \]
Using the sine value:
\[ \sin(37^\circ) \approx 0.6018 \]
\[ a = 20 \times 0.6018 \approx 12.036 \]
Therefore:
\[ a \approx 12 \, \text{m} \]
(Note: Round the answer to the nearest whole number.)
---
### Answer:
\( a = \boxed{12} \, \text{m} \)
---
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