00:01
So in this problem, you're told that you have a right triangle.
00:03
So why don't we go ahead and draw that? so here's our right triangle.
00:06
And here's our right angle.
00:08
And we want to find the missing side lengths.
00:11
If a is opposite angle a, b is opposite angle b, and c is the hypotenuse.
00:15
So let's say that we have a, b, and c.
00:20
Or this really should be a capital c.
00:22
So c is our hypotenuse.
00:23
Side a is opposite angle a.
00:25
And side b is opposite angle b.
00:28
Now, we're told that the tangent of angle a is equal to 5 twelfths.
00:31
Remember, that's the ratio of the adjacent side, so that's here, divided by the opposite side, which would be down here.
00:38
But keep in mind that b is equal to 2, so we know what this length is.
00:44
So what we need to do is we need to make this into a proportion to figure out the side of length a.
00:49
So first off, we have the adjacent side over the opposite side is 5 twelfths, but we know that the adjacent side is actually equal to 2.
00:57
We can find a by setting up this proportion.
01:01
Proportion.
01:01
So to solve for a, let's cross multiply.
01:03
5 times a is 5a...