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Chapter 4: Problem 81

Convert each angle measure to decimal degree form without using a calculator. Then check your answers using a calculator. (a) \(54^{\circ} 45^{\prime}\) (b) \(-128^{\circ} 30^{\prime}\)

Short Answer

Expert verified
The decimal degree equivalent of \(54^{\circ} 45^{\prime}\) is \(54.75^{\circ}\) and the decimal degree equivalent of \(-128^{\circ} 30^{\prime}\) is \(-128.5^{\circ}\).

Step by step solution

01

Convert Angle Measure to Decimal Degree

The angle is given as \(54^{\circ} 45^{\prime}\). Since 1 degree is equivalent to 60 minutes, the decimal degree equivalent would be \(54 + \frac{45}{60}\) degrees.
02

Simplify The Fraction

Simplify the fraction to get the decimal degree equivalent. \(54 + \frac{45}{60} = 54 + 0.75 = 54.75^{\circ}\). The decimal degree equivalent of \(54^{\circ} 45^{\prime}\) is \(54.75^{\circ}\).
03

Convert Second Angle Measure to Decimal Degree

The angle is given as \(-128^{\circ} 30^{\prime}\). Using the same process as above, the decimal degree equivalent would be \(-128 + \frac{30}{60}\) degrees.
04

Simplify The Fraction

Simplify the fraction to get the decimal degree equivalent. \(-128 + \frac{30}{60} = -128 + 0.5 = -128.5^{\circ}\). The decimal degree equivalent of \(-128^{\circ} 30^{\prime}\) is \(-128.5^{\circ}\).

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