Right Angled Triangles

The relationship

• Pythagoras' theorem links the three sides of a right-angled triangle, and it works in no other triangle
• The longest side is the hypotenuse, and it is always the one opposite the right angle
• The theorem states a² + b² = c², in which c stands for the hypotenuse while a and b stand for the other two sides
• Whichever of those two you call a and whichever you call b makes no difference to the result

• Papers do not use the words "Pythagoras" or "hypotenuse" in the question: they simply give a right-angled triangle with two sides marked

Using it both ways

• To find the hypotenuse, square both shorter sides, add, then take the square root
• To find a shorter side, square the hypotenuse and the known shorter side, subtract, then take the square root
• Adding when you should subtract is the standard error, and the check is simple: the hypotenuse must come out as the longest side

• Where an answer does not work out exactly, leave it as a surd if the question asks for an exact value, and otherwise round as instructed
• Cut a bigger figure into right-angled pieces and the theorem applies again, so dropping a perpendicular inside an isosceles triangle or a trapezium opens it up