Solve for the specified value of the following right triangle. Round your answer to the nearest hundredth. If A = 34° and a = 55 m, find c. 45.60 m 98.36 m 66.34 m 30.76 m
Solve for the specified value of the following right triangle. Round your answer to the nearest hundredth. If A = 34° and a = 55 m, find c. 45.60 m 98.36 m 66.34 m 30.76 m
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Mathematics Problem: Solving for the Hypotenuse of a Right Triangle**
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### Problem Statement
Solve for the specified value of the following right triangle. Round your answer to the nearest hundredth. If \( A = 34° \) and \( a = 55 \, \text{m} \), find \( c \).
1. \( 45.60 \, \text{m} \)
2. \( 98.36 \, \text{m} \)
3. \( 66.34 \, \text{m} \)
4. \( 30.76 \, \text{m} \)
### Approach
To solve for \( c \) (the hypotenuse) in a right triangle where an angle \( A \) and the length of the side opposite to it (\( a \)) are given, use the following formula derived from trigonometric ratios:
\[ \sin(A) = \frac{a}{c} \]
Rearranging the formula to solve for \( c \) gives:
\[ c = \frac{a}{\sin(A)} \]
1. Convert \( A \) to radians if necessary, though in this problem we will use degrees.
2. Calculate \(\sin(34°)\).
3. Divide \( a \) by \(\sin(34°)\) to find \( c \).
### Solution
1. Calculate \(\sin(34°)\):
\[ \sin(34°) \approx 0.5592 \]
2. Substitute the values into the equation:
\[ c = \frac{55 \, \text{m}}{0.5592} \approx 98.36 \, \text{m} \]
### Answer
The correct rounded value of \( c \) is \( \mathbf{98.36 \, \text{m}} \).
From the provided options, the correct choice is:
\[ \odot \, 98.36 \, \text{m} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1af3b856-d446-4ff7-a63e-89e70c8da553%2F7fc5f1da-7ba1-4325-92a3-727eacc0d4b6%2Fjwkmqed_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematics Problem: Solving for the Hypotenuse of a Right Triangle**
---
### Problem Statement
Solve for the specified value of the following right triangle. Round your answer to the nearest hundredth. If \( A = 34° \) and \( a = 55 \, \text{m} \), find \( c \).
1. \( 45.60 \, \text{m} \)
2. \( 98.36 \, \text{m} \)
3. \( 66.34 \, \text{m} \)
4. \( 30.76 \, \text{m} \)
### Approach
To solve for \( c \) (the hypotenuse) in a right triangle where an angle \( A \) and the length of the side opposite to it (\( a \)) are given, use the following formula derived from trigonometric ratios:
\[ \sin(A) = \frac{a}{c} \]
Rearranging the formula to solve for \( c \) gives:
\[ c = \frac{a}{\sin(A)} \]
1. Convert \( A \) to radians if necessary, though in this problem we will use degrees.
2. Calculate \(\sin(34°)\).
3. Divide \( a \) by \(\sin(34°)\) to find \( c \).
### Solution
1. Calculate \(\sin(34°)\):
\[ \sin(34°) \approx 0.5592 \]
2. Substitute the values into the equation:
\[ c = \frac{55 \, \text{m}}{0.5592} \approx 98.36 \, \text{m} \]
### Answer
The correct rounded value of \( c \) is \( \mathbf{98.36 \, \text{m}} \).
From the provided options, the correct choice is:
\[ \odot \, 98.36 \, \text{m} \]
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