b Which equation correctly uses the value of b to solve Triangle ABC is a right triangle and cos(22.6°)= 13 for a? Solve for b and round to the nearest whole number. O tan(22.6°) = 13 C 13 O tan(22.6°) = a B. 22.6 O tan(22.6°) = 13 cm 12 O tan(22.6°) =
b Which equation correctly uses the value of b to solve Triangle ABC is a right triangle and cos(22.6°)= 13 for a? Solve for b and round to the nearest whole number. O tan(22.6°) = 13 C 13 O tan(22.6°) = a B. 22.6 O tan(22.6°) = 13 cm 12 O tan(22.6°) =
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
![### Right Triangle Trigonometry Problem
**Problem Statement:**
Triangle ABC is a right triangle, and \(\cos(22.6^\circ) = \frac{b}{13}\).
**Tasks:**
- Solve for \(b\) and round to the nearest whole number.
- Identify which equation correctly uses the value of \(b\) to solve for \(a\).
**Given Diagram:**
- Triangle ABC is right-angled at C.
- \(AC = b\) (adjacent side to angle \(22.6^\circ\))
- \(BC = a\) (opposite side to angle \(22.6^\circ\))
- \(AB = 13\) cm (hypotenuse)
- \(\angle CAB = 22.6^\circ\)
Below is a depiction of the triangle:
```
C
/|
/ |
/ |
/ |
A /____| B
22.6° 13 cm
```
**Solving for \(b\):**
Using the cosine function definition: \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\)
Given:
\[
\cos(22.6^\circ) = \frac{b}{13}
\]
To solve for \(b\):
\[
b = 13 \times \cos(22.6^\circ)
\]
Using a calculator to find \(\cos(22.6^\circ)\):
\[
\cos(22.6^\circ) \approx 0.9239
\]
Therefore:
\[
b \approx 13 \times 0.9239 \approx 12.01
\]
Rounded to the nearest whole number:
\[
b \approx 12
\]
**Identifying the Correct Equation to Solve for \(a\):**
Looking at the given options:
- \(\tan(22.6^\circ) = \frac{a}{13}\)
- \(\tan(22.6^\circ) = \frac{13}{a}\)
- \(\tan(22.6^\circ) = \frac{a}{12}\)
- \(\tan(22.6^\circ) = \frac{12}{a}\)
Using the tangent function definition: \(\tan(\theta) = \frac{\text{opposite}}{\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2Faa8dec8c-49b6-4d9b-931b-a303e4b94a74%2Ftz7rcko_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Right Triangle Trigonometry Problem
**Problem Statement:**
Triangle ABC is a right triangle, and \(\cos(22.6^\circ) = \frac{b}{13}\).
**Tasks:**
- Solve for \(b\) and round to the nearest whole number.
- Identify which equation correctly uses the value of \(b\) to solve for \(a\).
**Given Diagram:**
- Triangle ABC is right-angled at C.
- \(AC = b\) (adjacent side to angle \(22.6^\circ\))
- \(BC = a\) (opposite side to angle \(22.6^\circ\))
- \(AB = 13\) cm (hypotenuse)
- \(\angle CAB = 22.6^\circ\)
Below is a depiction of the triangle:
```
C
/|
/ |
/ |
/ |
A /____| B
22.6° 13 cm
```
**Solving for \(b\):**
Using the cosine function definition: \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\)
Given:
\[
\cos(22.6^\circ) = \frac{b}{13}
\]
To solve for \(b\):
\[
b = 13 \times \cos(22.6^\circ)
\]
Using a calculator to find \(\cos(22.6^\circ)\):
\[
\cos(22.6^\circ) \approx 0.9239
\]
Therefore:
\[
b \approx 13 \times 0.9239 \approx 12.01
\]
Rounded to the nearest whole number:
\[
b \approx 12
\]
**Identifying the Correct Equation to Solve for \(a\):**
Looking at the given options:
- \(\tan(22.6^\circ) = \frac{a}{13}\)
- \(\tan(22.6^\circ) = \frac{13}{a}\)
- \(\tan(22.6^\circ) = \frac{a}{12}\)
- \(\tan(22.6^\circ) = \frac{12}{a}\)
Using the tangent function definition: \(\tan(\theta) = \frac{\text{opposite}}{\
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