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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Question
![**Problem Statement:**
Find the length of \( b \).
**Triangle Details:**
- Triangle \( \triangle ABC \) is given.
- Angle \( \angle CAB = 88^\circ \).
- Angle \( \angle ABC = 29^\circ \).
- Side \( AC = 16 \) units.
- Side \( AB = b \).
**Objective:**
Calculate the length of \( b \) and round it to the nearest tenth.
**Solution Explanation:**
To find the length of side \( b \), use the Law of Sines:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
- Given:
\[
A = 88^\circ, \quad B = 29^\circ
\]
- Find angle \( C \):
\[
C = 180^\circ - 88^\circ - 29^\circ = 63^\circ
\]
- Length \( c = 16 \).
Use the Law of Sines to find \( b \):
\[
\frac{b}{\sin B} = \frac{c}{\sin C}
\]
\[
b = \frac{16 \times \sin 29^\circ}{\sin 63^\circ}
\]
**Round the result to the nearest tenth** to find \( b \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2217feda-f3ce-4da8-88f2-e0417efc386d%2Fd81e743a-a1f1-44e2-9a20-115552278818%2Fu5kyfkq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the length of \( b \).
**Triangle Details:**
- Triangle \( \triangle ABC \) is given.
- Angle \( \angle CAB = 88^\circ \).
- Angle \( \angle ABC = 29^\circ \).
- Side \( AC = 16 \) units.
- Side \( AB = b \).
**Objective:**
Calculate the length of \( b \) and round it to the nearest tenth.
**Solution Explanation:**
To find the length of side \( b \), use the Law of Sines:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
- Given:
\[
A = 88^\circ, \quad B = 29^\circ
\]
- Find angle \( C \):
\[
C = 180^\circ - 88^\circ - 29^\circ = 63^\circ
\]
- Length \( c = 16 \).
Use the Law of Sines to find \( b \):
\[
\frac{b}{\sin B} = \frac{c}{\sin C}
\]
\[
b = \frac{16 \times \sin 29^\circ}{\sin 63^\circ}
\]
**Round the result to the nearest tenth** to find \( b \).
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