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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Question
![### Finding the Measure of Side b
**Task:**
Determine the length of side \( b \).
**Diagram Explanation:**
A right triangle \( \triangle ABC \) is illustrated with:
- \( \angle A \) labeled as \( 32^\circ \).
- \( \angle C \) as the right angle ( \( 90^\circ \) ).
- Hypotenuse \( \overline{AB} \) labeled as 290 inches.
- \( \overline{AC} \) and \( \overline{CB} \) as legs, with \( \overline{CB} \) labeled as \( b \).
**Steps to Solve:**
To solve for \( b \), use the trigonometric relation:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
For angle \( \angle A = 32^\circ \):
\[ \cos(32^\circ) = \frac{b}{290} \]
Rearranging to solve for \( b \):
\[ b = 290 \times \cos(32^\circ) \]
Use a calculator to find \( \cos(32^\circ) \):
\[ \cos(32^\circ) \approx 0.848 \]
Then:
\[ b = 290 \times 0.848 \approx 246 \text{ inches} \]
Therefore:
\[ b = 246 \text{ in.} \]
*(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%2Fdff355b9-f5dc-48f4-974a-8c516dd57c29%2Fc0bwzss_processed.png&w=3840&q=75)
Transcribed Image Text:### Finding the Measure of Side b
**Task:**
Determine the length of side \( b \).
**Diagram Explanation:**
A right triangle \( \triangle ABC \) is illustrated with:
- \( \angle A \) labeled as \( 32^\circ \).
- \( \angle C \) as the right angle ( \( 90^\circ \) ).
- Hypotenuse \( \overline{AB} \) labeled as 290 inches.
- \( \overline{AC} \) and \( \overline{CB} \) as legs, with \( \overline{CB} \) labeled as \( b \).
**Steps to Solve:**
To solve for \( b \), use the trigonometric relation:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
For angle \( \angle A = 32^\circ \):
\[ \cos(32^\circ) = \frac{b}{290} \]
Rearranging to solve for \( b \):
\[ b = 290 \times \cos(32^\circ) \]
Use a calculator to find \( \cos(32^\circ) \):
\[ \cos(32^\circ) \approx 0.848 \]
Then:
\[ b = 290 \times 0.848 \approx 246 \text{ inches} \]
Therefore:
\[ b = 246 \text{ in.} \]
*(Round the answer to the nearest whole number.)*
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