Calculate the Missing Sides of a Triangle Using Pythagoras' Theorem

Pythagoras' Theorem states that:

 

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

 

Thus, in the above right-angled triangle:  a² + b² = c²

 

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

 

Example 1

Use Pythagoras' Theorem to calculate the length of the hypotenuse, c, in the following right-angled triangle.  Give your answer to 3 significant figures.

 

 

Answer

By Pythagoras' Theorem:

c² = 3² + 8²

c² = 9 + 64

c² = 73

c = √73

c = 8.54 (to 3 s.f.)

 

Example 2

Use Pythagoras' Theorem to calculate the length of the side, a, in the following right-angled triangle.  Give your answer to 3 significant figures.

 

 

Answer

By Pythagoras' Theorem:

a² + 5² = 9²

a² + 25 = 81

a² = 81 - 25 = 56

a = √56

a = 7.48 (to 3 s.f.)

 

Let's try some questions now.