Pythagoras Q3

A plane leaves airport A and flies directly north for 30km to airport B where it turns on a bearing of 090 degrees and flies for 40km to airport C.

How far is airport A from airport C?

SOLUTION

The first thing to do is to draw a diagram.

We can now use Pythagoras' Theorem as follows:

So, airport A is 50km from airport C.

Notice that we have 3 integer values for the 3 lengths i.e. we have a Pythagorean Triple 30, 40, 50.

Pythagorean Triples

As you saw from question 1 the value of x was a whole number.  When we have 3 sides of a right angled triangle that are all integers (whole numbers) we call this set of values a Pythagorean Triple.

E.g. 3, 4, 5

E.g. 5, 12, 13

The length of the hypotenuse is 5 cm

Pythagoras Q1

Find the length of the hypotenuse.

The hypotenuse is 13 cm.