Question
Write the angle in decimal degrees. \( 31^{\circ} 42^{\prime} \) \( 31^{\circ} 42^{\prime}=\square^{\circ} \) (Type an integer or an exact decimal. If the decimal does not terminate, round to the nearest hundredth.)
Ask by Chadwick Collins.
Feb 02,2025 04:23
UpStudy AI Solution
Tutor-Verified Answer
Answer
\( 31.7^{\circ} \)
Solution
To convert \( 31^{\circ} 42^{\prime} \) to decimal degrees:
1. **Understand the Conversion:**
- There are 60 minutes in one degree.
- Therefore, \( 42^{\prime} \) can be converted to degrees by dividing by 60.
2. **Calculate:**
\[
42^{\prime} = \frac{42}{60} = 0.7^{\circ}
\]
3. **Add to the Degrees:**
\[
31^{\circ} + 0.7^{\circ} = 31.7^{\circ}
\]
So,
\[
31^{\circ} 42^{\prime} = 31.7^{\circ}
\]
**Answer:**
\( 31.7^{\circ} \)
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Simplify this solution The Deep Dive
To convert \( 31^{\circ} 42^{\prime} \) into decimal degrees, you'll need to convert the minutes into a fraction of a degree. Since there are 60 minutes in a degree, you can calculate:
\[
42^{\prime} = \frac{42}{60} = 0.7
\]
Now, add this to the 31 degrees:
\[
31^{\circ} + 0.7^{\circ} = 31.7^{\circ}
\]
Therefore, the final answer is \( 31.70^{\circ} \).
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