  # Pythagoras' Theorem (3)

In this worksheet, students 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

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

c = 7.48 (to 3 s.f.)

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