Solve for the specified value of the following right triangle. Round your answer to the nearest hundredth. If A = 42° and c = 89 cm, find b. 80.14 cm 59.55 cm 70.32 cm O 66.14 cm
Solve for the specified value of the following right triangle. Round your answer to the nearest hundredth. If A = 42° and c = 89 cm, find b. 80.14 cm 59.55 cm 70.32 cm O 66.14 cm
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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![**Example Problem: Solving a Right Triangle**
**Problem Statement:**
Solve for the specified value of the following right triangle. Round your answer to the nearest hundredth. If \( A = 42^\circ \) and \( c = 89 \, \text{cm} \), find \( b \).
**Options:**
1. \( 80.14 \, \text{cm} \)
2. \( 59.55 \, \text{cm} \)
3. \( 70.32 \, \text{cm} \)
4. \( 66.14 \, \text{cm} \)
**Explanation:**
In a right triangle, \( c \) represents the hypotenuse, while \( A \) represents one of the acute angles. To solve for \( b \) (the side opposite angle \( A \)), we can use the sine function from trigonometry, because sine relates the angle to the ratio of the opposite side over the hypotenuse:
\[ \sin(A) = \frac{b}{c} \]
Given:
- \( A = 42^\circ \)
- \( c = 89 \, \text{cm} \)
We need to find \( b \):
\[ \sin(42^\circ) = \frac{b}{89 \, \text{cm}} \]
Rearranging to solve for \( b \):
\[ b = 89 \, \text{cm} \times \sin(42^\circ) \]
Using a calculator to find \( \sin(42^\circ) \):
\[ \sin(42^\circ) \approx 0.6691 \]
Thus:
\[ b = 89 \, \text{cm} \times 0.6691 \]
\[ b \approx 59.55 \, \text{cm} \]
**Answer:**
\( b \approx 59.55 \, \text{cm} \)
So, the correct option is:
2. \( 59.55 \, \text{cm} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1af3b856-d446-4ff7-a63e-89e70c8da553%2F82ec7de6-e81d-4250-a8ac-febbc698e042%2F9b94kd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example Problem: Solving a Right Triangle**
**Problem Statement:**
Solve for the specified value of the following right triangle. Round your answer to the nearest hundredth. If \( A = 42^\circ \) and \( c = 89 \, \text{cm} \), find \( b \).
**Options:**
1. \( 80.14 \, \text{cm} \)
2. \( 59.55 \, \text{cm} \)
3. \( 70.32 \, \text{cm} \)
4. \( 66.14 \, \text{cm} \)
**Explanation:**
In a right triangle, \( c \) represents the hypotenuse, while \( A \) represents one of the acute angles. To solve for \( b \) (the side opposite angle \( A \)), we can use the sine function from trigonometry, because sine relates the angle to the ratio of the opposite side over the hypotenuse:
\[ \sin(A) = \frac{b}{c} \]
Given:
- \( A = 42^\circ \)
- \( c = 89 \, \text{cm} \)
We need to find \( b \):
\[ \sin(42^\circ) = \frac{b}{89 \, \text{cm}} \]
Rearranging to solve for \( b \):
\[ b = 89 \, \text{cm} \times \sin(42^\circ) \]
Using a calculator to find \( \sin(42^\circ) \):
\[ \sin(42^\circ) \approx 0.6691 \]
Thus:
\[ b = 89 \, \text{cm} \times 0.6691 \]
\[ b \approx 59.55 \, \text{cm} \]
**Answer:**
\( b \approx 59.55 \, \text{cm} \)
So, the correct option is:
2. \( 59.55 \, \text{cm} \)
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