00:01
All right, for this one, we're going to do a lot of algebra.
00:04
So first i'm going to write out with the angle of 25 degrees.
00:11
I have 800 plus this distance here, which is x.
00:15
We don't know it.
00:16
And then we've got our height h.
00:18
So i know that the tan of 25 degrees equals my opposite, which is my h, over 800 plus x.
00:30
If i look at this triangle right here, i know that the tan of 20 degrees.
00:34
9 equals h divided by x.
00:42
Okay.
00:43
I am not solving for x.
00:44
I want to know the height of the mountain.
00:46
And so i need to get one of these equations solved for x in terms of h so i can plug it into the other.
00:53
And so i'm going to do the bottom one here.
00:55
Multiply both sides by x.
00:58
So i have x times the tan of 29 equals h.
01:12
And then i'm going to divide by the t.
01:14
Tan of 29.
01:20
Okay, because now i have that x equals h divided by the tangent of 29.
01:29
Now what i'm going to do is i'm going to plug this in up here for x and then i'm going to solve it for h.
01:37
So i have the tan, and this is just going to be kind of an ugly process, so we'll just kind of walk through it together.
01:43
Tan of 25 equals h divided by 800 plus x, and x is really a little.
01:50
H divided by the tan of 29.
01:55
Okay.
01:57
I'm going to multiply both sides by this.
02:03
Okay, so i'm going to multiply it on the right and the left.
02:06
And so on the left, i'll just write it in green.
02:09
I have 800 plus h divided by the tan of 29, all times the tan of 25.
02:28
And this equals h, because on this.
02:30
Side that's going to cancel.
02:33
I'm going to distribute this in to both terms and so i have 800 tan 25 plus h times the tan of 25 divided by the tan of 29 and that's going to equal h.
02:58
I'm going to take this...