How to use sin, cos and tan continues…
.. with a video on finding the length of a missing side in a right angle triangle.
Watch the video and try the quick test.
Click here to try the Quick Test SohCahToa
As before you can use SOHCAHTOA to calculate the length of a missing side, although, in this case, you’ll need to:
- know the length of one side
- know the size of one of the acute angles
A typical exam question would be along the lines of –
‘Calculate the length of the side marked ‘a.’ Give your answer to 3 significant figures’
With these type of questions it’s better to have a series of steps:
- label the side opposite to the angle
- label the hypotenuse (longest side)
- label the side adjacent to the angle you want to work out
- use SohCahToa – in this question we are going to use Soh
- Once you’ve calculated – check it! – side ‘a’ must be shorter than the hypotenuse. 6.43cm looks about right.
Many of the practical applications of this type of maths come from surveying – perhaps finding out the length or height of something when it’s very difficult to measure. Try this example; suppose we want to find out the height of a tower:
The surveyor can measure the angle, from 5m away, as 32 degrees. Therefore:
.. we can use trigonometry to find out the exact height – in this case the tan rule – Toa:
Using a calculator 5 x tan 32 = 3.124. So the height of the tower is 3.125 + the surveyors height of 1.72m:
Total height = 4.844m
Total height = 4.8m (to 2 s.f.)
Here’s some other posts that might be of interest: