Question

Express the following angle in degree, minutes, and seconds: \[\left( {321.9} \right)^\circ \].

Answer 1

Hint:
Here, we need to express the given angle as an angle in degrees, minutes and seconds. We will write the given angle as a sum of a natural number, and the numbers in the decimal place. Then, we will convert the second number with the decimal places to minutes using the relation between degrees and minutes, to get the angle in degrees and minutes. Similarly, any remaining decimal places in the minutes can be converted to seconds to get the angle in degrees, minutes and seconds. 1 degree is equal to 60 minutes.

Complete step by step solution:
We can write the angle \[\left( {321.9} \right)^\circ \] as the sum of \[321^\circ \] and \[\left( {0.9} \right)^\circ \].
Therefore, we get
\[ \Rightarrow \left( {321.9} \right)^\circ = 321^\circ + \left( {0.9} \right)^\circ \]
First, we will convert \[\left( {0.9} \right)^\circ \] to minutes.
We know that 1 degree is equal to 60 minutes.
Therefore, we get
60 minutes \[ = \] 1 degree
Now, multiplying both sides of the equation by \[0.9\], we get
\[\left( {60 \times 0.9} \right)\]minutes \[ = \left( {1 \times 0.9} \right)\] degree
Thus, we get
\[54\] minutes \[ = 0.9\]degree
Now, we can use the value of \[0.9\] degree in minutes in the equation \[\left( {321.9} \right)^\circ = 321^\circ + \left( {0.9} \right)^\circ \] to write the given angle in degrees and minutes.
Substituting \[\left( {0.9} \right)^\circ = 54\]minutes in the equation \[\left( {321.9} \right)^\circ = 321^\circ + \left( {0.9} \right)^\circ \], we get
\[ \Rightarrow \left( {321.9} \right)^\circ = 321^\circ + 54\] minutes
Minutes are denoted by the symbol.
Rewriting the equation, we get

Therefore, we have expressed \[\left( {321.9} \right)^\circ \] as in degrees, minutes.

Note:
We expressed \[\left( {321.9} \right)^\circ \] as an angle in degrees and minutes. The value of \[0.9\] degree in minutes is 54 minutes. Since 54 is a natural number, and not in a decimal form, we cannot convert it to seconds. If we convert all 54 minutes to seconds, then the answer will be in degrees and seconds. Unless the minutes are in decimal, there is no need to convert the minutes to seconds.