Find the missing side lengths and angle measures given the following information. Round your answers to the nearest tenth. B = 28.3°, C = 90°, and c = 62.4 in. Use the paperclip button below to attach files.
Find the missing side lengths and angle measures given the following information. Round your answers to the nearest tenth. B = 28.3°, C = 90°, and c = 62.4 in. Use the paperclip button below to attach files.
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 missing side lengths and angle measures given the following information. Round your answers to the nearest tenth. B = 28.3°, C = 90°, and c = 62.4 in.
---
**Solution:**
Given:
- Angle B = 28.3°
- Angle C = 90°
- Side c (opposite angle C) = 62.4 in
1. **Calculate Angle A:**
Since the sum of angles in a triangle is 180°,
\[ A = 180° - B - C \]
\[ A = 180° - 28.3° - 90° \]
\[ A = 61.7° \]
2. **Calculate Side b:**
(Using tangent function, because tangent is opposite/adjacent, and angle B is opposite side a and adjacent to side c)
\[
\tan(B) = \frac{a}{c}
\]
\[
\tan(28.3°) = \frac{a}{62.4}
\]
\[
a = \tan(28.3°) \times 62.4
\]
Using a calculator,
\[
a \approx \tan(28.3°) \times 62.4 \approx 62.4\times 0.5383 \approx 33.6 \text{ in}
\]
3. **Calculate Side a:**
(Using Pythagorean theorem, \(a^2 + b^2 = c^2\))
\[
a = \sqrt{c^2 - b^2}
\]
\[
a = \sqrt{62.4^2 - 33.6^2}
\]
\[
a = \sqrt{3889.76 - 1128.96}
\]
\[
a = \sqrt{2760.8}
\]
\[
a \approx 52.5
\]
---
**Summary of Results:**
- Angle A = 61.7°
- Side a ≈ 52.5 in
- Side b ≈ 33.6 in
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F846a5d83-ebd2-4e0d-9bf0-b0f470211899%2F7964c590-9bc4-43fd-b588-26f7bb7d1f80%2F33888rk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the missing side lengths and angle measures given the following information. Round your answers to the nearest tenth. B = 28.3°, C = 90°, and c = 62.4 in.
---
**Solution:**
Given:
- Angle B = 28.3°
- Angle C = 90°
- Side c (opposite angle C) = 62.4 in
1. **Calculate Angle A:**
Since the sum of angles in a triangle is 180°,
\[ A = 180° - B - C \]
\[ A = 180° - 28.3° - 90° \]
\[ A = 61.7° \]
2. **Calculate Side b:**
(Using tangent function, because tangent is opposite/adjacent, and angle B is opposite side a and adjacent to side c)
\[
\tan(B) = \frac{a}{c}
\]
\[
\tan(28.3°) = \frac{a}{62.4}
\]
\[
a = \tan(28.3°) \times 62.4
\]
Using a calculator,
\[
a \approx \tan(28.3°) \times 62.4 \approx 62.4\times 0.5383 \approx 33.6 \text{ in}
\]
3. **Calculate Side a:**
(Using Pythagorean theorem, \(a^2 + b^2 = c^2\))
\[
a = \sqrt{c^2 - b^2}
\]
\[
a = \sqrt{62.4^2 - 33.6^2}
\]
\[
a = \sqrt{3889.76 - 1128.96}
\]
\[
a = \sqrt{2760.8}
\]
\[
a \approx 52.5
\]
---
**Summary of Results:**
- Angle A = 61.7°
- Side a ≈ 52.5 in
- Side b ≈ 33.6 in
---
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