
Now, I'm being a little cryptic here.

What do I mean by "ratios?"

Let's go back to our similar triangles to figure out what I mean.

Now, I have two triangles here.

They're similar because the angles match,

but the sides are different.

I'm going to label these sides a, b, c and these sides A, B, and C.

You can see that even though these sides are all longer,

there's some correspondence between A and side a.

Likewise with C and c and B and b.

But what exactly is that correspondence?

What do these things all have in common?

The fact is they have a ratio in common.

What I mean by that is they're linked through ratios.

If I look at the ratio side A to side B,

I'm going to find that's exactly the same as the ratio of side a to side b.

In fact, it doesn't matter how big or small I make this triangle,

this equality will always hold true.

And that's a really powerful mathematical tool that we can use.

For example, let's say I didn't give you variable names here,

but I gave you some actual numbers.

So, 3 m, 4 m and 5 m are replacing our sides from before,

and these are still unknown.

But let's say I told you thatI don't knowside B was equal to 6 m.

I can use this to calculate side C,

because I know that C/B has to equal, well, the corresponding sides4/3.

More precisely 4 m over 3 m.

Notice that when we do this, the units cancel out,

so it doesn't even matter that we were using meters.

We could have been using inches or stadia or furlongs or any unit we'd like.

Now, I know this ratioC/Bis equal to 4/3.

But notice that I have one other piece of information.

B is actually equal to 6 m, so let's write that in.

Now if I want to solve for C, I multiply both sides by 6 m,

and that gives me the following: C = 4/3 * 6 m, also known as 8 m.

Okay, that wasn't so bad.

We used the power of ratios to calculate an unknown side of a triangle,

and this is a huge tool to have at our disposal.

Can you do the same to solve for side A?

How long is side A in meters.

And you can just enter the number. You don't have to type in the m.