I learned how to do this problem in Geometry... but I just can't get it right now. Or at least, the Algebra is too complex for me. Anyway, here's the problem, then I will tell you how far I got.

Using a sextant, a surveyor determines that the angle of elevation of a mountain peak is 35 degrees. Moving 1000 feet further away from the mountain, the surveyor determines the angle of elevation to be 30 degrees. What is the mountain's height?

After drawing a nice little picture, I gathered that tan 30=y/(1000+x), with x being the distance between the surveyor's first recording and the middle of the mountain (the peak, then straight down).

My second equation was tan 35=y/x, for reasons that can be extracted from the picture.

So, my two equations:
tan30=y/(1000+x)
tan35=y/x

I do realize that there is a certain equation into which I could magically memorize and plug in numbers and out pops an answer. I do not know it, and my notes are too illegible to decipher the equation. Also, my natural curiosity gets the better of me when I tried to work out this simple system.

So, this is how far I got:

x=y/tan35... so:
tan30=y/(1000+(y/tan35))... then
(tan30)(1000+(y/tan35))=y
1000tan30+(tan30y/tan35)=y
1000tan30=y-(tan30y/tan35)

My notes indicate (remember that my handwriting is horrid) that the next step would be to write this:

1000tan30=h((1-tan30)/tan35)

This makes no sense to me, and I can think of no other way to solve this algebra problem... without muddling it up even more than it already is... perhaps if I multiplied both sides by tan35/y... even still it would be muddled. Maybe not. Let me see.
Even if I do get the answer, the magic equation would be nice.
I have no desire to continue this Algebraic madness all the way through my homework...

Also, as a side-note, I am in AP Pre-Cal... kids these days aren't learning this stuff in Geometry :)

Thanks in advance,
qazaq

You have:

tan 35 = y/x and tan 30 = y/(x + 1000).

Solve both of these for y in terms of x:

y = x*tan 35 and y = (x + 1000)*tan 30

Then set them equal to each other:

x*tan 35 = (x + 1000)*tan 30

Solve for x, then calculate y by plugging your value for x into y = x*tan 35

That is an incredibly easy way to do it. Wow, thank you.

I think the formula my math teacher mentioned is actually not really worth even memorizing...

Great, I got 3,296.526 ft... there is still quite a bit of algebra involved... ah well