Unit 3 Section 4 : Problems in Context
When solving problems using Pythagoras' Theorem, the key step is to draw a rightangled triangle.
Example Question
A ship sails 300 km due west and then 100 km due south.
At the end of this journey, how far is the ship from its starting position?
The first step is to draw a diagram showing the ship's starting position and the route it has taken:
We can see that the two parts of the journey form the two shorter sides of a rightangled triangle.
Now we need to use Pythagoras' Theorem to find the length of the hypotenuse, d.
Follow the steps below to work out each stage of the calculation, then click
to see whether you are correct.
Write down Pythagoras' Theorem with the relevant values : 

Work out the squares of the two shorter sides : 

Add together the two values on the right : 

Find the square root of both sides : 

Exercises
Work out the answers to the questions below and fill in the boxes. Click on the
button to find out whether you have answered correctly. If you are right
then will appear and you should move on to the next
question. If appears then your answer is wrong. Click
on to clear your original answer and have another go.
If you can't work out the right answer then click on
to see
the answer.
You will find it helpful to draw a diagram for each question showing the rightangled triangle.
You have now completed Unit 3 Section 4
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