Algebra (Period 1)

PYTHAGOREAN THEOREM 11-7
(an old friend) -
FOR RIGHT TRIANGLES ONLY!
2 legs - make the right angle - called ‘a’ and ‘b’
(doesn't matter which is which because you will add them and adding is COMMUTATIVE!)
hypotenuse - longest side across from the right angle - called ‘c’
You can find the third side of a right triangle as long as you know the other two sides:
a² + b² = c²
After squaring the two sides that you know, you'll need to find the square root of that number to find the length of the missing side (that's why it's in this chapter!)

EASIEST - FIND THE HYPOTENUSE (c)
Example #1 from p. 510
8² + 15² = c²
64 + 225 = c²
289 = c²
c = 17

A LITTLE HARDER - FIND A MISSING LEG (Either a or b)
Example #5 from p. 510
5² + b² = 13²
25 + b² = 169
b² = 169 - 25
b² = 144
b = 12

ONE THAT YOU WOULDN'T HAVE HAD IN PRE-ALGEBRA:
One of the legs = √5
√5² + b² = 13²
5 + b² = 169
b² = 169 - 5
b² = 164
√ b2 = √164
b = √4•41
b = 2√41
There are many real life examples where you can use the Pythagorean Theorem to find a length.

EXAMPLE: HOW HIGH A 10 FOOT LADDER REACHES ON A HOUSE
A 10 ft ladder is placed on a house 5 ft away from the base of the house.
Find how high up the house the ladder reaches.
The ladder makes a right triangle with the ground being one leg, the house the other, and the ladder is the hypotenuse ( see drawing in #1 on p. 515)
You need to find the distance on the house, so you're finding one leg.

ANOTHER EXAMPLE:
You're flying your kite for the kite project and you want to know how long the kite string must be so that it can reach a height of 13 ft in the air if you're standing 9 feet away from where the kite is in the air.
The string represents the hypotenuse.
You know one leg is the height in the air (13 ft) and the other leg is how far on the ground you are standing away from where the kite is flying (9 ft)
You need to find the hypotenuse.