(32° 44') + (28° 21')
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![**Addition of Angles in Degrees and Minutes**
To add two angles given in degrees (°) and minutes (′), follow these steps:
### Problem:
**Add as indicated.**
\[ (32^\circ 44′) + (28^\circ 21′) \]
### Solution:
To add these angles:
1. **Addition of Minutes**: Start with the minutes (′).
```
44′ + 21′ = 65′
```
2. **Conversion**: Since 60 minutes make 1 degree, convert 65 minutes to degrees.
```
65′ = 60′ + 5′ = 1^\circ 5′
```
3. **Addition of Degrees**: Add the degrees, including the converted degree from minutes.
```
32^\circ + 28^\circ + 1^\circ (from minutes) = 61^\circ
```
4. **Final Result**: Combine the degrees and remaining minutes.
```
61^\circ 5′
```
### Visual Guide:
**Given:**
\[ (32^\circ 44′) + (28^\circ 21′) \]
- **Step 1:** Add the minutes: \( 44′ + 21′ = 65′ \).
- **Step 2:** Convert 65 minutes to degrees: \( 65′ = 1^\circ 5′ \) (since 60 minutes make 1 degree).
- **Step 3:** Add degrees: \( 32^\circ + 28^\circ + 1^\circ (from minutes) = 61^\circ \).
- **Step 4:** Combine the degrees and minutes: \( 61^\circ 5′ \).
**Result:**
\[ (32^\circ 44′) + (28^\circ 21′) = 61^\circ 5′ \]
This process illustrates the step-by-step addition of angles in degrees and minutes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F643de4d0-ca3c-47ed-94f6-02fd3fafa065%2F4a4a2d8a-4fbc-4719-8591-e165fda5a447%2Fnxln13l.jpeg&w=3840&q=75)
Transcribed Image Text:**Addition of Angles in Degrees and Minutes**
To add two angles given in degrees (°) and minutes (′), follow these steps:
### Problem:
**Add as indicated.**
\[ (32^\circ 44′) + (28^\circ 21′) \]
### Solution:
To add these angles:
1. **Addition of Minutes**: Start with the minutes (′).
```
44′ + 21′ = 65′
```
2. **Conversion**: Since 60 minutes make 1 degree, convert 65 minutes to degrees.
```
65′ = 60′ + 5′ = 1^\circ 5′
```
3. **Addition of Degrees**: Add the degrees, including the converted degree from minutes.
```
32^\circ + 28^\circ + 1^\circ (from minutes) = 61^\circ
```
4. **Final Result**: Combine the degrees and remaining minutes.
```
61^\circ 5′
```
### Visual Guide:
**Given:**
\[ (32^\circ 44′) + (28^\circ 21′) \]
- **Step 1:** Add the minutes: \( 44′ + 21′ = 65′ \).
- **Step 2:** Convert 65 minutes to degrees: \( 65′ = 1^\circ 5′ \) (since 60 minutes make 1 degree).
- **Step 3:** Add degrees: \( 32^\circ + 28^\circ + 1^\circ (from minutes) = 61^\circ \).
- **Step 4:** Combine the degrees and minutes: \( 61^\circ 5′ \).
**Result:**
\[ (32^\circ 44′) + (28^\circ 21′) = 61^\circ 5′ \]
This process illustrates the step-by-step addition of angles in degrees and minutes.
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