 EXT Degrees, Minutes and Seconds in Angles

Lesson

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.

Remember!

There are $60$60 minutes in $1$1 degree.

There are $60$60 seconds in $1$1 minute.

Converting decimals to minutes and seconds

To convert a decimal into minutes and seconds, we need to find what decimal

For example, let's say we wanted to round $15.72^\circ$15.72° to the nearest minute.

We need to work 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^\circ$15°$43$43'. Converting on a calculator

The button highlighted in blue allows you to write degrees and minutes in your calculator.

The button highlighted in green will convert between decimals and minutes/seconds.

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.

Worked Examples

Question 1

Round $25^\circ$25°$49$49'$40$40" to the nearest minute.

1. $\editable{}$° $\editable{}$'

Question 2

Convert the following into degrees and minutes:

1. $24.4^\circ$24.4°=$\editable{}$ degrees $\editable{}$ minutes

Question 3

Given $10\cos x=7$10cosx=7:

1. Find the value of $x$x correct to two decimal places.

2. Hence find $x$x to the nearest minute.

Question 4

Consider the following diagram. 1. Find the value of $x$x correct to 2 decimal places.

2. Hence find $x$x to the nearest minute.