Pythagoras Theorem
A cat is trapped on a tree that is standing perpendicular (at a right angle) to the ground. The tree is 3 meters tall. A fireman is here to rescue the cat, and he knows the cat is going to jump and soar downwards for 5 meters downwards before hitting the ground. From the base of the tree, how far must the fireman run in order to save the cat? Pythagoras Theorem This basically states for every right-angled triangle, the sum of the square of two sides add up to the square of the longest side (called the hypotenuse).
In other words,
a^2+b^2=c^2
Uses: We can use this to find the distance of missing sides, or to find out if a triangle is a right-angled triangle or not. We just have to substitue the values into a,b and c to see if everything works out. How many meters away from the base of the tree? We know the tree is 3 meters, and the longest side is 5 meters. (a and b does not matter for now!) So let's substitute things in:
3^2+b^2=5^2
9+b^2=25
Rearrange:
25-9=b^2
16=b^2
Square root both sides to get:
b=4
And now you know the fireman must stand directly four meters away from the tree to catch the falling cat!
