Chapter 4.1, Problem 76E

To determine

Find the difference of the two given angles ${\text{81}}^{0}17\text{'}\text{'}$ and $36{}^{0}8\text{'}43\text{'}\text{'}$

Answer to Problem 76E

  $44{}^{0}51\text{'}34\text{'}\text{'}$

Explanation of Solution

Given: Two angles ${\text{81}}^{0}17\text{'}\text{'}$ and $36{}^{0}8\text{'}43\text{'}\text{'}$

Concept Used:

Formally, the number being subtracted is known as the subtrahend, while the number it is subtracted from is the minuend. The result is the difference.

We can write: minuend - subtrahend = difference.

For subtraction we can use the formulas: $\begin{array}{l}{1}^0=60\text{minutes}\\ 1\text{minute}=60\text{seconds}\end{array}$

Calculation:

We know that: $1^0=60\text{'}$ and $1\text{'}=60\text{'}\text{'}$

In this Problem Minuend (the first angle) has only seconds. We can rewrite the first angle in ${\text{D}}^{\text{0}}\text{M'}\text{S''}$ .

  $\begin{array}{l}{\text{81}}^{0}17\text{'}\text{'}={\text{80}}^0+1^0+17\text{'}\text{'}={\text{80}}^0+60\text{'}+17\text{'}\text{'}[1^0=60\text{'}]\\ ={\text{80}}^0+59\text{'}+1\text{'}+17\text{'}\text{'}\\ ={\text{80}}^0+59\text{'}+60\text{'}\text{'}+17\text{'}\text{'}[1\text{'}=60\text{'}\text{'}]\\ {\text{81}}^{0}17\text{'}\text{'}={\text{80}}^0+59\text{'}+77\text{'}\text{'}\end{array}$

We know that       Difference::

  $\begin{array}{l}{1}^0=60\text{minutes}\\ 1\text{minute}=60\text{seconds}\end{array}$ $\begin{array}{l}{80}^{0}59\text{'}77\text{'}\text{'}\\ -\underrightarrow{36{}^{0}08\text{'}43\text{'}\text{'}}\\ 44{}^{0}51\text{'}34\text{'}\text{'}\end{array}$

Thus, the difference of two angles ${\text{81}}^{0}17\text{'}\text{'}$ and $36{}^{0}8\text{'}43\text{'}\text{'}$ is $44{}^{0}51\text{'}34\text{'}\text{'}$