Question

Express in degrees, minutes and seconds the given angle: $8{}^\circ $ .

Answer 1

Hint: We will first write how many minutes and seconds there are in one degree, and then we will look at the given expression and if there is no decimal part then it has only degrees, no minutes and second. If it has a decimal part then the number before decimal is the degree and for the number after decimal we will use the relation between degree minutes and second to convert the decimal into minutes and second.

Complete step-by-step answer:
Let’s start our solution by first writing the relation between degree to minutes and seconds.
First we will use the minute of arc method for the relation between degree and minute.
A minute of arc or arcminute is a unit of angular measurement equal to $\dfrac{1}{60}$ of $1{}^\circ $ .
Therefore, from this we get $60\min =1{}^\circ $ .
Now we will use the second of the arc method to form the relation between degree and second.
A second of arc is $\dfrac{1}{60}$ of arcminute which is $\dfrac{1}{3600}$ of $1{}^\circ $.
Therefore, from this we get $3600\sec =1{}^\circ $ .
Hence the degree has been converted to minutes and second, and we have the result that we need to solve this question.
Now we have given $8{}^\circ $and there is no decimal part so there will not be any minutes and seconds.
Therefore, the answer in degree, minutes and seconds is: $8{}^\circ 0'0''$ .

Note: The conversion method that we have used to convert degrees to minutes and seconds is very important. The end result that we have got must be remembered to avoid any mistakes while solving the question. In some questions instead of degree, minutes and seconds it is given DMS, so one should not be confused in such cases.