Chapter 4.1, Problem 67E

To determine

Convert ${64}^{0}45\text{'}$ into decimal degree form.

Answer to Problem 67E

  $64{.75}^0$

Explanation of Solution

Given: The angle ${64}^{0}45\text{'}$

Concept Used:

Degree is a measure of an angle. One degree is one 360th part of a full circle.

Each degree is split up into 60 parts, each part being 1/60 of a degree. These parts are called minutes.

Each minute is split up into 60 parts, each part being 1/60 of a minute. These parts are called seconds.

One degree is 60 minutes. One minute is 60 seconds. 360 degrees is the same as a complete circle around north-south axis or from the equator.

Relation between degree and minute $60\text{minutes}=1^0$

Calculation:

  $\begin{array}{l}60\text{minutes}=1^0\\ 1\text{minute}\text{=}\frac{1}{60}\mathrm{deg}\\ 45\min \text{ute}s=45·\frac{1}{60}\mathrm{deg}=\frac{45}{60}\mathrm{deg}=\frac{3}{4}\mathrm{deg}=0.75\mathrm{deg}\\ {64}^{0}45\text{'}={64}^0+45\text{'}={64}^0+{0.75}^0=64{.75}^0\end{array}$

Thus, ${64}^{0}45\text{'}$ is equal to $64{.75}^0$