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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help finding the measure of the indicated angle.
**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
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
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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