  # Calculate the Missing Sides of a Triangle Using Pythagoras' Theorem

In this worksheet, students will find the length of the missing side of right-angled triangles using Pythagoras' Theorem. Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Solve Right-Angled Triangle Problems

Popular topics:   Geometry worksheets

Difficulty level:   #### Worksheet Overview

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. 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. 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.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started #### Popular Maths topics

• • • • 