Chapter 10, Problem 1P

Convert angles between decimal degrees and degrees and minutes.

1. (a) Convert 43.4° to degrees and minutes.
2. (b) Convert 65°15′ to decimal degrees.

To determine

To write: The angle $43.4°$ in degrees and minutes.

Answer to Problem 1P

The angle $43.4°$ can be written in degrees and minutes as $\underset{\_}{43°24^{\prime }}$.

Explanation of Solution

The given angle is $43.4°$.

Step 1:

Write the angle as the sum of whole number and decimal as,

$43.4°=43°+0.4°$.

Step 2:

Covert it to degrees and minute using the unity fraction as,

$\begin{array}{c}43°+0.4°=43°+\left(0.4°\times \frac{60^{\prime }}{1°}\right)\left(\because 60^{\prime }=1°\right)\\ =43°+\left(0.4\right)60^{\prime }\\ =43°24^{\prime }\end{array}$

Thus, the angle $43.4°$ can be written in degrees and minutes as $\underset{\_}{43°24^{\prime }}$.

To determine

To write: The angle $65°15^{\prime }$ in decimal degrees.

Answer to Problem 1P

The angle $65°15^{\prime }$ can be written in decimal degrees as $\underset{\_}{65.25°}$.

Explanation of Solution

The given angle is $65°15^{\prime }$.

Step 1:

Write the angle as the sum of degrees and minutes as,

$65°15^{\prime }=65°+15^{\prime }$.

Step 2:

Covert the minutes to degrees using the unity fraction as,

$\begin{array}{c}65°+15^{\prime }=65°+\left(15^{\prime }\times \frac{1°}{60^{\prime }}\right)\left(\because 60^{\prime }=1°\right)\\ =65°+\left(\frac{15}{60}\right)\left(1°\right)\\ =65.25°\end{array}$

Thus, the angle $65°15^{\prime }$ can be written in decimal degrees as $\underset{\_}{65.25°}$.