Solve Problems in Right-Angled Triangles Using Pythagoras' Theorem

In this activity, we are going to use Pythagoras' Theorem to solve problems with right-angled triangles. 

 

You will need a calculator for this activity.

 

Let's start with a recap on the formula!

 

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

  a² + b² = c²

 

 

 

Remember, the triangle must be right-angled and the hypotenuse is always the longest side which is opposite the right angle.

 

Let's have a look at a problem!

 

Example

Calculate the perimeter of the right-angled triangle below.

 

 

Answer

When we look at this problem we think about perimeter first.

To get the perimeter of the triangle we need to add up all the sides.

 

We only know two sides, so we need to use Pythagoras' Theorem to find the hypotenuse!

 

  a² + b² = c²

 

Using Pythagoras' Theorem:

a² + b² = c²

6² + 8² = c²

c² = 36 + 64 = 100

c = √100

c = 10 cm

 

Not quite finished!

 

Perimeter = 6 + 8 + 10 = 24 cm

 

 

Let's have a go at some questions!