00:01
All right, in your question here, you're asked to find h.
00:04
And to find h, we're going to need to throw in another variable here.
00:08
I'm going to call this unknown distance x from here to here.
00:14
And to start with, i'm going to set up a tangent ratio using the 20 .5 angle.
00:21
Tangent of 20 .5 is going to equal the opposite side, h, over the adjacent side.
00:28
We have to act like that whole triangle base is included here and that's going to be x plus 378 and then we're going to set up a tangent ratio for the 52 .3 and it's going to equal h over x now i'm going to solve both of these problems for h by multiplying by the denominator on both sides okay so that cancels out and we have i'm going to write it as h equals x plus 378 times tangent of 20 .5.
01:15
Now the second one, we multiply both sides by x, and we're going to have h equals x times tangent of 52 .3.
01:29
Now what you want to do is you want to use substitution, since we have a system of equations, i'm going to substitute this expression in for the h in the second problem.
01:45
Okay, so now that becomes x plus 378 times tangent of 20 .5 is going to equal x times tangent of 52 .3.
02:02
And i'm saving this to type into my calculator as far as i can.
02:06
So now i'm going to distribute the tangent inside here.
02:11
So i have x tangent of 20 .5 plus 378 tangent of 20 .5 equals x tangent of 52 .3.
02:27
And then anything that has an x, i'm going to move this one by subtracting it.
02:34
I want to get it together with the other x.
02:43
And now we have the equation 378 tangent of 20 .5...