Measuring Angles

An important part of working in Geometry and Measurement is the use of angles.

  1. Write down the units we use to measure angles and the symbol.
  1. Look at the right angled triangle below: (Note: the angle is labelled with the Greek letter theta(). Greek letters are commonly used as pronumerals in Geometry)

a)Double the length of sides a and c, then join them and measure the length of the new line parallel to side b.

How much larger than b is the new line?

b)If the angle  does not change, what will happen to the length of the vertical side if sides a and c are made larger and larger?

c)If an astronomer has been told that there is a one degree distance between two stars in the sky, and the astronomer is not very good at being accurate with measuring angles, what problem might be encountered?

d)Do you think that if the astronomer is one degree out that if will make much difference to her observations? Why?

  1. Mathematicians and Scientists need to be more accurate than to the nearest degree, so just like we divide up metres into smaller parts (cm and mm),each degree is dividedinto 60 equal parts – minutes, and each minute into 60 seconds, just like time. This makes conversions a bit tricky because it isn’t metric, but we can write degrees either as decimals eg: 43.5 or as 4330 (43 degrees, 30 minutes) Remember 0.5 of a degree is half a degree or 30 minutes.

a)Convert the following decimal angles into degrees and minutes.

23.5 =14.75 = 72.25 =

b)Estimate the following decimal angles into degrees and minutes.

37.4 = 105.9 = 3.1 =

c)Convert the following angles into decimal form.

1830 = 2515 = 7645 =

d)Estimate the following angles in decimal form.

2921 = 1741 = 566 =

Now ask someone to show you how to use a scientific calculator to convert between degrees, minutes, seconds and decimal degrees.