Perform each calculation. See Example 3. 90° ― 17° 13'

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Convert the angle 17° 13' into decimal degrees. To do this, divide the minutes by 60 since there are 60 minutes in a degree. So, 13' becomes \( \frac{13}{60} \) degrees.

Add the converted minutes to the degrees: \( 17 + \frac{13}{60} \) degrees.

Now, subtract the decimal degree value obtained from 90°.

Perform the subtraction: \( 90° - (17 + \frac{13}{60})° \).

The result will give you the angle in decimal degrees.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Angle Measurement

Angles can be measured in degrees or radians, with degrees being the most common unit. A full circle is 360 degrees, and angles can also be expressed in degrees, minutes, and seconds (DMS). In this format, 1 degree equals 60 minutes, and 1 minute equals 60 seconds. Understanding how to convert between these units is essential for accurate calculations.

Subtraction of Angles

Subtracting angles involves taking one angle measurement away from another. When dealing with angles in DMS format, it is important to ensure that the minutes and seconds are properly converted if the subtraction results in a negative value. This concept is crucial for performing calculations involving angles, especially when they are expressed in different formats.

Conversion Between DMS and Decimal Degrees

Converting angles from degrees, minutes, and seconds to decimal degrees is often necessary for calculations. The formula for conversion is: Decimal Degrees = Degrees + (Minutes/60) + (Seconds/3600). This conversion allows for easier arithmetic operations and is particularly useful when performing angle subtraction or addition.

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