SOLUTION: A rocket carrying a weather satellite is launched. As it moves through space, the rocket is tracked by two tracking stations located 24 km apart, beneath the rocket. The two tracki

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Question 622224: A rocket carrying a weather satellite is launched. As it moves through space, the rocket is tracked by two tracking stations located 24 km apart, beneath the rocket. The two tracking stations both lie west of the launching pad and are located on a straight line from the launching pad. At a specific moment, the rocket's angle of elevation from Station X is 40 degrees while the rocket's angle of elevation from Station Y is 70 degrees. Both tracking stations are west of the rocket at this moment. At this moment, what is the altitude of the rocket, correct to one decimal place?

Thanks In Advance!

So far I have this, I am not quite sure where to take it from here! Thanks
Sin 40 = x/24
24 x Sin 40 = 15.3
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Draw out the picture. It's always a good idea to draw out the picture (as accurately as you can) even if you have no idea what to do or where to go.
A drawing may help you see what you have to do.

Our goal is to find h. But to do that, we need to find w. We can use the tangent function to say that

tan(70) = opp/adj

tan(70) = h/w

Then solve for w to get

w = h/tan(70)

w = h/2.747477

w = 0.36397h

Now we can say

tan(40) = h/(x+w)

tan(40) = h/(24+w) ... Note: x = 24 as it's given that the two stations are 24 km apart.

tan(40) = h/(24+0.36397h)

From here, you can solve for h (since that's the only variable left). I'll let you do this.