Solve Problems in Right-Angled Triangles by 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

A square has side length of 4 cm

Calculate the length of the diagonal.

Answer to 1 decimal place.

Answer

If we look at the square , the diagonal cuts it into two right-angled triangles.

The sides we know are both 4 cm.

Using Pythagoras' Theorem:

a² + b² = c²

4² + 4² = c²

c² = 16 + 16 = 32

c = √32

c = 5.7 (1 dp)

Let's have a go at some questions!