QUESTION 1 Convert the angle written in DMS to decimal degrees: 2830 48' 14". Report below the answer in three decimal places.
QUESTION 1 Convert the angle written in DMS to decimal degrees: 2830 48' 14". Report below the answer in three decimal places.
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter44: Solution Of Equations By The Subtraction, Addition, And Division Principles Of Equality
Section: Chapter Questions
Problem 38A
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
100%
![### Question 1
**Convert the angle written in DMS to decimal degrees: 283° 48' 14''.**
Report below the answer in three decimal places.
---
#### Solution:
To convert an angle from degrees, minutes, and seconds (DMS) to decimal degrees, follow these steps:
1. **Understand the components:**
- Degrees (°): 283°
- Minutes ('): 48'
- Seconds ("): 14''
2. **Convert minutes to degrees:**
- There are 60 minutes in a degree, so divide the minutes by 60.
\[ 48' = \frac{48}{60} = 0.8° \]
3. **Convert seconds to degrees:**
- There are 3600 seconds in a degree, so divide the seconds by 3600.
\[ 14'' = \frac{14}{3600} \approx 0.003889° \]
4. **Add these values to the initial degrees:**
\[ 283° + 0.8° + 0.003889° \approx 283.803889° \]
5. **Round to three decimal places:**
\[ 283.804° \]
**Final Answer: 283.804°**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ec67c7b-35f9-46ad-9f6f-16823e234ec7%2F1eba1cd5-4fa4-4d12-a77e-24dcb88e473a%2Fwgvvlf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 1
**Convert the angle written in DMS to decimal degrees: 283° 48' 14''.**
Report below the answer in three decimal places.
---
#### Solution:
To convert an angle from degrees, minutes, and seconds (DMS) to decimal degrees, follow these steps:
1. **Understand the components:**
- Degrees (°): 283°
- Minutes ('): 48'
- Seconds ("): 14''
2. **Convert minutes to degrees:**
- There are 60 minutes in a degree, so divide the minutes by 60.
\[ 48' = \frac{48}{60} = 0.8° \]
3. **Convert seconds to degrees:**
- There are 3600 seconds in a degree, so divide the seconds by 3600.
\[ 14'' = \frac{14}{3600} \approx 0.003889° \]
4. **Add these values to the initial degrees:**
\[ 283° + 0.8° + 0.003889° \approx 283.803889° \]
5. **Round to three decimal places:**
\[ 283.804° \]
**Final Answer: 283.804°**
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
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
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL