(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°.
icon
Related questions
Question
100%
**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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Types of Angles
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry
Algebra and Trigonometry
Trigonometry
ISBN:
9781938168376
Author:
Jay Abramson
Publisher:
OpenStax
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning