Algebra Period 3 (Thursday & Friday)

USING THE PYTHAGOREAN THEOREM - WORD PROBLEMS: 11-8
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.

EQUATIONS WITH RADICALS: 11-9
When you have an equation where the variable is under the √ sign,
simply square both sides to solve for the variable.

This is actually similar to regular equation balancing!
The goal is still to find out what the variable is.
But to find it, you need to ISOLATE the √ with the variable first
Then you square


Example #1 on p. 521
√x = 5
Square both sides and you'll get x = 25

Example # 9 is much harder
3 + √(x - 1) = 5
move the 3 to other side first √(x - 1) = 5 - 3
Now square both sides x - 1 = 22
Now add 1 to both sides: x = 4 + 1 x = 5

Look at Examples #15 & 16 ---- In both cases, there is no possible value for x because the square root of a number CAN NEVER BE NEGATIVE IN THE REAL NUMBER SYSTEM!

Try Example #17 yourself, and see what happens (you should also end up with no value, but why?)

Need to review how to estimate the value of square roots--Check out the blog post on March 16th.