Convert the angle measure 62◦ 33 to decimal degree form.
The Correct Answer and Explanation is :
To convert the angle 62° 33′ to decimal degree form, we follow a systematic method. This involves separating the degrees (°) from the minutes (‘) and converting the minutes into a fraction of a degree.
Step-by-Step Process:
- Start with the given angle:
The angle is provided in degrees and minutes, where:
- 62° is the degree part
- 33′ is the minute part
- Convert the minutes into a decimal:
The minute (‘) is a unit of angular measurement, and there are 60 minutes in a degree. To convert minutes into a decimal form, divide the number of minutes by 60.
[
33′ = \frac{33}{60} = 0.55
] - Add the converted decimal to the degree part:
Now, add the decimal from the previous step to the degree part:
[
62° + 0.55 = 62.55°
]
Thus, 62° 33′ in decimal degrees is 62.55°.
Explanation of the Conversion:
In geographical or mathematical calculations, angles are often represented in degrees, minutes, and seconds (DMS). Each degree is divided into 60 minutes, and each minute is divided into 60 seconds. While this format is often used for precise measurements, decimal degrees are commonly used in many modern applications, such as GPS and mapping systems, because they are easier to work with computationally.
In decimal degree form, the minutes are expressed as a fraction of 60. This is why converting minutes into decimals simplifies operations involving angular measurements. Once converted, the value becomes easier to process in calculations and can be input directly into many digital tools without needing additional conversions.
Thus, by dividing the minutes by 60 and adding that result to the degree, we can accurately convert angles from DMS to decimal degrees. This form is widely used in cartography, navigation, and in any field requiring precise angular measurements.