Pythagoras' Theorem

What is the formula for Pythagoras' Theorem?

a² + b² = c², where c is the hypotenuse and a and b are the shorter sides.

When are you allowed to use Pythagoras' Theorem?

Only on right-angled triangles when working purely with side lengths (no angles involved).

What is the definition of the hypotenuse?

The longest side of a right-angled triangle, located directly opposite the 90° right angle.

What is the formula to calculate the hypotenuse (c)?

c = √(a² + b²)

What is the formula to calculate a shorter side (a or b)?

a = √(c² - b²)

How do you calculate the distance between two coordinates (x1, y1) and (x2, y2)?

d = √((x2 - x1)² + (y2 - y1)²)

What is the 3D Pythagoras formula for finding a cuboid's internal diagonal?

d = √(l² + w² + h²), where l = length, w = width, h = height.

What are the step-by-step actions to solve a 3D Pythagoras problem?

1. Use 2D Pythagoras on the base to find the floor diagonal. 2. Use 2D Pythagoras vertically using the floor diagonal and the height.