What Is The Hypotenuse?
The hypotenuse is the longest side of the right angle triangle. It is directly opposite the right-angle symbol. The hypotenuse is used for trigonometry. The sine ratio and cosine ratio involve the hypotenuse side of the triangle.
What Is Pythagoras' Theorem?
The pythagoras theorem states that a² + b² = c². c is always the longest side of the triangle called the hypotenuse (see above). In the example below the hypotenuse is 5 cm, a equates to 3 cm, b equates to 4 cm. It is true that 3² (9), plus 4² (16) equals 5², 25.
Pythagoras Example Question 1
The image below shows an example of a pythagoras question. The missing side is labelled x and it is the hypotenuse. Since 6² (36) adding to 8² (64) equals 10² (100) then the missing side x is 10 cm.
Pythagoras Example Question 2
The missing side in pythagoras question 2 is x. This time x is not the hypotenuse. The hypotenuse is given and it is 13 cm. The final answer is 12 cm because 13² (169) minus 5² (25) is 144 and the square root of 144 is 12.
Pythagorean triples are useful to remember. For example if two sides of a right angle triangle measure 3 units and 4 units the longest side measures 5 units. When side a measures 5 units and side b measures 12 units then the hypotenuse measures 13 units.