s) Find the height, h, of the roof, rounded to the nearest 16th of an inch using the n Theorem. 15'- 4" A° 28'-8" Find the angle A°, to the nearest tenth.
s) Find the height, h, of the roof, rounded to the nearest 16th of an inch using the n Theorem. 15'- 4" A° 28'-8" Find the angle A°, to the nearest tenth.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 75RE
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Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
Find the height, h, of the roof, rounded to the nearest 16th of an inch using the Pythagorean Theorem.
find the angle A, to the nearest tenth.
![### Educational Content on Roof Geometry & the Pythagorean Theorem
#### Problem Statement and Diagram Interpretation
**Question:**
a. Find the height, \(h\), of the roof, rounded to the nearest 1/16th of an inch using the Pythagorean Theorem.
b. Find the angle \(A\degree\), to the nearest tenth.
#### Diagram Description:
The provided diagram is a right triangle with the following dimensions and labels:
- Hypotenuse: 15 feet 4 inches
- Base: 28 feet 8 inches
- Height: \(h\) (to be determined)
- Angle \(A\degree\) (to be determined)
#### Steps to Solve:
1. **Using the Pythagorean Theorem to Find \(h\):**
The Pythagorean Theorem states \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\) and \(b\) are the other two sides of a right triangle.
- Convert the dimensions to the same unit (inches for better precision):
- 28 feet 8 inches = \(28 \times 12 + 8 = 344\) inches
- 15 feet 4 inches = \(15 \times 12 + 4 = 184\) inches
- Apply the Pythagorean Theorem:
\[
h^2 + 344^2 = 184^2
\]
\[
h^2 = 184^2 - 344^2
\]
\[
h = \sqrt{184^2 - 344^2}
\]
2. **Finding Angle \(A\degree\):**
Use trigonometric ratios such as tangent, sine, or cosine.
\[
\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{184}
\]
\[
A = \arcsin\left(\frac{h}{184}\right)
\]
**Note:** For precise solving, use a scientific calculator to determine numerical values and round your answers as specified in the question.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e9c998a-5af1-4bc2-b298-e1462b059995%2Fbfe71b54-4c06-4ba1-a538-c207c3c9901f%2Fqafoqss_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content on Roof Geometry & the Pythagorean Theorem
#### Problem Statement and Diagram Interpretation
**Question:**
a. Find the height, \(h\), of the roof, rounded to the nearest 1/16th of an inch using the Pythagorean Theorem.
b. Find the angle \(A\degree\), to the nearest tenth.
#### Diagram Description:
The provided diagram is a right triangle with the following dimensions and labels:
- Hypotenuse: 15 feet 4 inches
- Base: 28 feet 8 inches
- Height: \(h\) (to be determined)
- Angle \(A\degree\) (to be determined)
#### Steps to Solve:
1. **Using the Pythagorean Theorem to Find \(h\):**
The Pythagorean Theorem states \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\) and \(b\) are the other two sides of a right triangle.
- Convert the dimensions to the same unit (inches for better precision):
- 28 feet 8 inches = \(28 \times 12 + 8 = 344\) inches
- 15 feet 4 inches = \(15 \times 12 + 4 = 184\) inches
- Apply the Pythagorean Theorem:
\[
h^2 + 344^2 = 184^2
\]
\[
h^2 = 184^2 - 344^2
\]
\[
h = \sqrt{184^2 - 344^2}
\]
2. **Finding Angle \(A\degree\):**
Use trigonometric ratios such as tangent, sine, or cosine.
\[
\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{184}
\]
\[
A = \arcsin\left(\frac{h}{184}\right)
\]
**Note:** For precise solving, use a scientific calculator to determine numerical values and round your answers as specified in the question.
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