Must Know
Use the Pythagorean Theorem to find the missing lengths of Right-Angled Triangles
A right-angled triangle is a particular triangle which has two really important features:
One of its interior angles is 90°, also known as a right-angle. The right-angle is often shown as a small square box in the corner of the triangle
The side opposite the right-angle is always the longest side of the triangle and is called the hypotenuse
Because of their special properties, right-angled triangles are really useful helping us solve different problems. Here are a few examples:
Finding the lengths of lines on a grid
Finding the heights of isosceles triangles
Finding the heights of large objects in real life
We're almost ready to start solving problems using the Pythagorean Theorem, but before that we need to make sure we understand how to square and square root numbers using a calculator.
Squaring a number means we multiply it by itself. For example 3 squared is written as 3² and it means 3 x 3, therefore 3² = 9, because 3 x 3 = 9.
The square root of a number is generally a smaller number that you can square (multiply by itself) to get the bigger number. For example the square root of 64 is written like this: √64. What number when squared gives us 64? Well 8 x 8 = 64, so √64 = 8.
Below you can find these buttons on some of the more common calculators:
You made it - now we can finally start learning about the Pythagorean Theorem and how we can use it to solve problems! The Pythagorean Theorem explore the special relationship between the three side lengths of a right-angled triangle. Check out this video which demonstrates this visually.
These might be a little tricky, but try and use your knowledge of Pythagoras to attempt these 3D Pythagoras problems. The trick is to form a 2D Right-Angled Triangle inside the 3D shape!