Chapter 4.1, Problem 48E

a.

To determine

Find the decimal degree for the given angle.

Answer to Problem 48E

The decimal degree for $-{135}^{°}36\text{'}\text{'}$ is $-{135.01}^{°}$ .

Explanation of Solution

Given:

The given angle is $-{135}^{°}36\text{'}\text{'}$ .

Calculation:

The conversion rule between seconds and degrees.

To convert seconds to degrees,

multiplyseconds by $\frac{1^{°}}{3600\text{'}\text{'}}$ .

To convert degrees to seconds

multiply degrees by $3600$ .

Now,

  $36\text{'}\text{'}=36\text{'}\text{'}\times \frac{1^{°}}{{3600}^{\text{'}\text{'}}}={0.01}^{°}$

Decimal degree for $-{135}^{°}36\text{'}\text{'}=-\left({135}^{°}+{0.01}^{°}\right)=-{135.01}^{°}$

Hence the decimal degree for $-{135}^{°}36\text{'}\text{'}$ is $-{135.01}^{°}$ .

b.

To determine

Find the decimal degree for the given angle.

Answer to Problem 48E

The decimal degree for $-{408}^{°}16\text{'}20\text{'}\text{'}$ is $-{408.272}^{°}$ .

Explanation of Solution

Given:

The given angle is $-{408}^{°}16\text{'}20\text{'}\text{'}$ .

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 $60$ .

  $16\text{'}=16\text{'}\times \frac{1^{°}}{{60}^{\text{'}}}={0.266667}^{°}$

The conversion rule between seconds and degrees.

To convert seconds to degrees,

multiply seconds by $\frac{1^{°}}{3600\text{'}\text{'}}$ .

To convert degrees to seconds

multiply degrees by $3600$ .

  $20\text{'}\text{'}=20\text{'}\text{'}\times \frac{1^{°}}{3600\text{'}\text{'}}={0.00555556}^{°}$

Decimal degree for $-{408}^{°}16\text{'}20\text{'}\text{'}=-\left({408}^{°}+0.266667+{0.00555556}^{°}\right)=-{408.272}^{°}$

Hence the decimal degree for $-{408}^{°}16\text{'}20\text{'}\text{'}$ is $-{408.272}^{°}$ .