Find the measure of the indicated angle to the nearest degree. (Whole Number). 19) 20) 44-Hyp 26 ору Cosc 39-Adj 33
Find the measure of the indicated angle to the nearest degree. (Whole Number). 19) 20) 44-Hyp 26 ору Cosc 39-Adj 33
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Concept explainers
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
I need help finding the measure of the indicated angle.
Transcribed Image Text:**Triangle Angle Calculation - Nearest Whole Number**
**Find the measure of the indicated angle to the nearest degree.**
---
**19)**
This problem involves a right-angled triangle. The sides are labeled as follows:
- Adjacent (Adj) to the angle: 39 units
- Hypotenuse (Hyp): 44 units
- Opposite (Opp): ?
The angle to be found is indicated with a question mark and points to the unknown angle. The trigonometric function used is cosine (cos).
Diagram:
```
?
/|
Hyp / | Opp
/ |
/-----|
Adj
```
- Hypotenuse = 44 units
- Adjacent = 39 units
---
**20)**
This problem involves another right-angled triangle. The sides are labeled as follows:
- Adjacent (Adj) to the angle: 33 units (base)
- Opposite (Opp): 26 units (height)
- Hypotenuse (Hyp): ?
The indicated angle to be found is represented by a question mark next to the horizontal leg.
Diagram:
```
?
/|
Hyp / |
/ | Opp
/-----|
Adj
```
- Adjacent = 33 units
- Opposite = 26 units
---
**21)**
The problem features a right-angled triangle. The sides are labeled:
- Adjacent (Adj) to the angle: 24 units (height)
- Opposite (Opp): ?
- Hypotenuse (Hyp): 36 units (base)
The indicated angle to be found is denoted by a question mark next to the vertical leg.
Diagram:
```
?
/|
Hyp/ | Adj
/ |
/----|
Opp
```
- Hypotenuse = 36 units
- Adjacent = 24 units
---
**22)**
This problem involves a right-angled triangle. The sides are labeled:
- Adjacent (Adj) to the angle: 23 units (base)
- Opposite (Opp): ?
- Hypotenuse (Hyp): 20 units (height)
The angle to be found is shown with a question mark at the base.
Diagram:
```
?
/|
Hyp / | Opp
/ |
/-----|
Adj
```
- Hypotenuse = 20 units
- Adjacent = 23 units
---
To identify the
![### Trigonometric Functions and Finding Angles
#### Example Problems
**Problem 19**
We are given a right triangle with:
- Hypotenuse (HYP) = 44
- Adjacent side (Adj) = 39
- Opposite side (Opp) = ?
We need to find the measure of the indicated angle, represented by "?".
Here's a step-by-step guide to finding the angle using trigonometric functions:
1. **Identify the trigonometric function to use**: Since we have the adjacent side (Adj) and hypotenuse (HYP), we can use the cosine function.
2. **Set up the equation using the cosine function**:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{39}{44}
\]
3. **Calculate the angle**: Find the inverse cosine (arccos) of the ratio to get the angle:
\[
\theta = \cos^{-1}\left(\frac{39}{44}\right)
\]
**Problem 21**
We are given another right triangle with:
- One leg is 24
- The other leg is 36
- Hypotenuse = ?
To find the measure of the indicated angle, represented by "?", we can either use the tangent (since we have both opposite and adjacent sides) or sine/cosine functions.
Here’s how you can solve it using the tangent function:
1. **Identify the trigonometric function to use**: Since we have both legs of the triangle (opposite and adjacent), use the tangent function.
2. **Set up the equation using the tangent function**:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{36}{24}
\]
3. **Calculate the angle**: Find the inverse tangent (arctan) of the ratio to get the angle:
\[
\theta = \tan^{-1}\left(\frac{36}{24}\right)
\]
#### Explanation of Diagrams:
- **Diagram 1 (Problem 19)**: A right-angled triangle labeled with a hypotenuse of 44, an adjacent side of 39, and an unknown opposite side. The right angle is marked, and the angle to find is labeled with a question](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a8da60f-e382-4aa0-a272-0f9664a6f8ac%2Fd14a2442-4f49-42a6-94d7-4da4d9a99ae2%2Fl3cp65q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometric Functions and Finding Angles
#### Example Problems
**Problem 19**
We are given a right triangle with:
- Hypotenuse (HYP) = 44
- Adjacent side (Adj) = 39
- Opposite side (Opp) = ?
We need to find the measure of the indicated angle, represented by "?".
Here's a step-by-step guide to finding the angle using trigonometric functions:
1. **Identify the trigonometric function to use**: Since we have the adjacent side (Adj) and hypotenuse (HYP), we can use the cosine function.
2. **Set up the equation using the cosine function**:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{39}{44}
\]
3. **Calculate the angle**: Find the inverse cosine (arccos) of the ratio to get the angle:
\[
\theta = \cos^{-1}\left(\frac{39}{44}\right)
\]
**Problem 21**
We are given another right triangle with:
- One leg is 24
- The other leg is 36
- Hypotenuse = ?
To find the measure of the indicated angle, represented by "?", we can either use the tangent (since we have both opposite and adjacent sides) or sine/cosine functions.
Here’s how you can solve it using the tangent function:
1. **Identify the trigonometric function to use**: Since we have both legs of the triangle (opposite and adjacent), use the tangent function.
2. **Set up the equation using the tangent function**:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{36}{24}
\]
3. **Calculate the angle**: Find the inverse tangent (arctan) of the ratio to get the angle:
\[
\theta = \tan^{-1}\left(\frac{36}{24}\right)
\]
#### Explanation of Diagrams:
- **Diagram 1 (Problem 19)**: A right-angled triangle labeled with a hypotenuse of 44, an adjacent side of 39, and an unknown opposite side. The right angle is marked, and the angle to find is labeled with a question
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