A boat is sailing toward shore, but, instead of a beach, there is a tall cliff at the place where the ocean meets the land. An observer on the boat measures the angle of elevation from the boat to the top of the cliff to be 14 degrees. The boat sails 600m closer to the cliff and the observer finds that the angle of elevation has changed to 19 degrees. Find the height of the cliff.

I got 542.21 meters. I know i'll be lucky to get one response, but it's finals time.
woot! geometry! actually it sucks but whatever. Sorry I would do the problem but I'm too lazy and I have other homework to do so tell me the answer.
I got 342.1
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That oughta do it.

Time for a supercool guitar demonstration by herman li,

Herman Li- why is this guitar so big?

Stage guy- because its a bass herman

seriously if my friend
billpurcell
was on he'd tell you in a second
similar triangles dude. draw a freakin picture and do the trig yourself. soh-cah-toa bs. i'd help but had a calc 2 test today, so I quit teh mathz
i got the same as you... h = [Sin(180-19)/Sin(19-14)]*Sin(14)*600
lol. we just did that in my Algebra II class. a question exactly like that.
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gimme a sec galen im on the phone w josh again and hes hihg
389.093 dude. duh.
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Tl:dr but skimmed.

Either law of sines or cosines.
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I forgot. I just finished that class with a semester average of 83... I'm pretty lucky.

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i got 558ish but idk. its a goofy problem just because it involves doing gay stuff with cotangents and stuff (at least how i did it). if you can figure out the correct answer i'd really like to see how its done the right way haha
i got 542.099586
i think this is simpler than u guys think, because i don't know what the hell you're talking about

tan 14 = x/(y + 600)
tan 19 = x/y

we work with the second equation and get:
x = y(tan19)

we plug that into the other and get

tan 14 = (y(tan19)) / (y + 600)

multiply both sides by y + 600 and get

ytan14 + 600tan14 = ytan19

if we call tan 19 = A and tan 14 = B, and subtract y(B) from both sides, making A - B = C, then

600B = yC

divide both sides by C,

and get 542.21

EDIT: looks like mr. purcell got it first, thanks
Yep, pretty positive it's 542.216m.

I used the Law of Sines to find the hypotenuse, then just used the sine function to find the height.
It's not a right triangle is it? Tl;dr.

So technically....It's not a hypotenuse...Right?
Gear...
Peavey 5150, Squier, Ibanez RG2EX2, Yamaha F150, Ibanez RT150, MXR noisegate