Chapter 4.1, Problem 47E

a.

To determine

Find the decimal degree for the given angle.

Answer to Problem 47E

The decimal degree for ${54}^{°}45\text{'}$ is ${54.75}^{°}$ .

Explanation of Solution

Given:

The given angle is ${54}^{°}45\text{'}$ .

Calculation:

The conversion rule between minutes and degrees.

To convert minutes to degrees,

multiplyminutes by $\frac{1^{°}}{60\text{'}}$ .

To convert degrees to minutes,

multiplydegrees by $60$ .

Now,

  $45\text{'}=45\text{'}\times \frac{1^{°}}{{60}^{\text{'}}}={0.75}^{°}$

Decimal degree for ${54}^{°}45\text{'}={54}^{°}+{0.75}^{°}={54.75}^{°}$

Hence the decimal degree for ${54}^{°}45\text{'}$ is ${54.75}^{°}$ .

b.

To determine

Find the decimal degree for the given angle.

Answer to Problem 47E

The decimal degree for $-{128}^{°}30\text{'}$ is $-{128.5}^{°}$ .

Explanation of Solution

Given:

The given angle is $-{128}^{°}30\text{'}$ .

Calculation:

The conversion rule between minutes and degrees.

To convert minutes to degrees,

multiply minutes by $\frac{1^{°}}{60\text{'}}$ .

To convert degrees to minutes,

multiply degrees by $60$ .

Now,

  $30\text{'}=30\text{'}\times \frac{1^{°}}{{60}^{\text{'}}}={0.5}^{°}$

Decimal degree for $-{128}^{°}30\text{'}=-\left({128}^{°}+{0.5}^{°}\right)=-{128.5}^{°}$

Hence the decimal degree for $-{128}^{°}30\text{'}$ is $-{128.5}^{°}$ .