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Chapter 4: Problem 47

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 forms of the given angles are:\n(a) \(54^{\circ} 45^{\prime}\) = \(54.75^{\circ}\)\n(b) \(-128^{\circ} 30^{\prime}\) = \(-128.5^{\circ}\)

Step by step solution

01

Convert (a) \(54^{\circ} 45^{\prime}\) to decimal degree

To convert minutes into decimal, divide the minutes by 60. Thus, \(45^{\prime} = \frac{45}{60} = 0.75\).\nNow combine this with the degree measure. So, \(54^{\circ} 45^{\prime}\) in decimal degrees will be \(54^{\circ} + 0.75^{\circ} = 54.75^{\circ}\).
02

Convert (b) \(-128^{\circ} 30^{\prime}\) to decimal degree

Similar to the previous step, convert the minutes by dividing by 60. So, \(30^{\prime} = \frac{30}{60} = 0.5\).\nCombine this with the degree measure. So, \(-128^{\circ} 30^{\prime}\) in decimal degrees will be \(-128^{\circ} - 0.5^{\circ} = -128.5^{\circ}\). Note that since the original degree was negative, the decimal is subtracted instead of added.
03

Verification with calculator

Although the exercise states not to use a calculator, the final step asks to verify the answers with a calculator. When performing the calculations on the calculator, make sure to divide the minutes by 60 to convert them into decimal form, then combine them with the degree measures. The calculator should return the same results as in Steps 1 and 2.

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