5.07 Extension: Degrees, minutes, seconds
We've already looked at how to find angles using trigonometric ratios and we are used to giving our answers as whole numbers or decimals. Now we are going to look at another way to express a part of a degree using minutes and seconds.
There are $60$60 minutes in $1$1 degree and we use ' to denote a minute.
There are $60$60 seconds in $1$1 minute and we use " to denote a second.
$45$45 degrees, $18$18 minutes and $3$3 seconds would be written as $45^\circ18'3"$45°18′3"
Worked example
Question 1
Evaluate: Round $15.72^\circ$15.72° to the nearest minute.
Think/Do: We need to find out $15^\circ$15° + $0.72$0.72 of a degree, which is $15^\circ$15° + $0.72$0.72 of a $60$60 minutes.
| $0.72\times60$0.72×60 | $=$= | $43.2$43.2 minutes |
So, $15.72^\circ$15.72° rounded to the nearest minute is $15^\circ43'$15°43′.
Rounding
Rounding minutes and seconds is similar to rounding decimals. However, because there are $60$60 minutes in a degree and $60$60 seconds in a minute, our half way point is $30$30.
- If the minutes are below $30$30, we round down to the nearest degree.
- If the minutes are $30$30 or above, we round up to the nearest degree.
- If the seconds are below $30$30, we round down to the nearest minute.
-
If the seconds are $30$30 or above, we round up to the nearest minute.
Practice questions
Question 2
Round $25^\circ$25°$49$49'$40$40" to the nearest minute.
$\editable{}$° $\editable{}$'
Question 3
Convert the following into degrees and minutes:
$24.4^\circ$24.4°=$\editable{}$ degrees $\editable{}$ minutes
Question 4
Given $10\cos x=7$10cosx=7:
Find the value of $x$x correct to two decimal places.
Hence find $x$x to the nearest minute.
Question 5
Consider the following diagram.
Find the value of $x$x correct to 2 decimal places.
Hence find $x$x to the nearest minute.