Pythagorean Theorem

The Pythagorean Theorem is used to find a missing side length of a right triangle. It only works for right triangles (one with a right angle).

The formula to use is a² + b² = c². A really good explanation of the formula and its derivation can be found here.

In order to use the theorem, you must know the parts of the triangle. Parts a and b of the theorem are the legs of the triangle. These are the side lengths that make up the right angle. The third side (longest side) is noted as c in the theorem.

Now substitute the values given into the theorem (formula) and solve the equation.

Example: A triangle has a side length of 6 cm and a side length of 8 cm. What is the length of the hypotenuse?

6² + 8² = c²
36 + 64 = c²
100 = c²
√100 = √c²
10 = c

Example: A triangle has a side length of 6 cm and a hypotenuse length of 12 cm. What is the length of the missing side?

a² + 6² = 12²
a² + 36 = 144
a² + 36 – 36 = 144 – 36
a² = 108
√a² = √108
a = √108
a = 6√3

Picture of triangle above from http://en.wikibooks.org/wiki/File:Right_triangle_shows_hyp_legs.PNG

Rate-Time-Distance Word Problems Part 2

Now for the second part of the rate-time-distance problems. This example refers to opposite direction travel.

Let’s look at the following example:

Train 1 leaves the train station travelling south at a rate of speed that is 10 mph more than train 2 which is travelling north. After 3 hours, they are 450 miles apart. Find the rate of train 2.

We are going to use another table to organize the rate, time and distance information.

Train	Rate	Time	Distance
1	r +10	3	3 (r + 10)
2	r	3	3r

Since the trains are moving in opposite directions, we are going to add their distances together to get 450 miles.

3 (r + 10) + 3r = 450
3r + 30 + 3r = 450
6r + 30 = 450
6r = 420
r = 70

Therefore the rate of train 2 is 70 mph.

Algebra Games On-line

Hey guys! I'm trying to find some good online games for my Algebra classes. I found the following site and it looked like it might be interesting. Let me know what you think.

http://www.onlinemathlearning.com/algebra-math-games.html

Ever Wonder About Dividing by Zero?

If you've ever wondered why you can't divide by zero, here is an explanation that uses what you learned in elementary school to help you understand this concept.

In elementary school, you learned that division is just multiplication fact families in an alternate order. In other words, 6/3 = 2 because 2 x 3 = 6.

We can use fact families to find out about dividing by zero.

0/7 = ?? The answer is 0, because 0 x 7 = 0.

What about 7/0? If you put this in your calculator, you'll get an error. Why?

Well, if we use fact families, 7/0 = ?? What number can you multiply by 0 to get 7? There isn't any number. So the answer is undefined.

Now you may be wondering about 0/0? The calculator still gives you an error. Shouldn't it have given you a 1 or maybe a 0? Isn't 7/7 =1? And 2/2=1?

Let's try fact families again to see what the answer should be. 0/0 = ??

What number multiplied by 0 = 0? Well, every number would work wouldn't it, so the answer is indeterminate. You can't determine what the answer should be.

Hopefully, this explanation has helped to clear up division by zero and why is doesn't work.

New Blog Created

I've created this new blog to help answer some of those tricky algebra questions that high school students have. I will be including articles that seem to give lots of students trouble. I currently teach Algebra I and have been doing so for several years. I'd like to provide assistance to those who need it so here goes! Welcome and please visit often.