Trigonometry fun!

[ResidentBiscuit]

Yes, this is homework. It's the one question I haven't gotten right on the assignment. I'm a perfectionist, I can't stand for having one question wrong when I can go back and redo it. So, don't tell me the answer. Just point me in the right direction. I've solved problems like this, just not going in this direction and for some reason I keep getting the wrong answer. So, here it is.

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 12° 38'. When the boat stops, the angle of depression is 50° 11' . The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

What I've tried was this:
Note: x1 is the distance between the light house and the 50 degree angle, x2 is the distance between the 50 degree angle and the 12 degree angle.

tan(12.633)= 200/x1+x2
tan(50.183)= 200/x1

x1*tan(12.633) + x2*tan(12.633) = x1*tan(50.1833)

0.244*x1 + 0.244*x2 = 1.1995*x1

//Combine like terms here... Not gonna show that, its obvious

x1 = (0.244/0.976)x2
So, x1 roughly= 1/4 x2

So, from here I found x1, since I have all the pertinent information for it. And then multiplied that by 4 (I even tried the reverse way, so I could preserve the exact number) to get x2, and it was wrong. I got

666.236

, which is not an answer.

[ResidentBiscuit]

Hmm, might have been going at this the wrong way actually. I just got another answer that is within .5 feet of an answer. So that could just be due to rounding and truncating throughout the process.

[NGen]

I got

666.236

Embrace satan and it will be your answer

[ResidentBiscuit]

Embrace satan and it will be your answer

I was going to, but it wasn't even an option :(

[ModShop]

You may find it easier to draw a diagram, then try to figure out the trig rather than just trying to figure it out.

http://www.freeimagehosting.net/vaajc

Then just play around with the angles/sides until you find the side you want.

[ne555]

IIRC you are marking the wrong angles.

I got 666.236, which is not an answer.

¿why not?

[atropos]

...Round your answer to the hundredths place.

...I got 666.236

Is 666.24 an answer? :P

On a more serious note, lemme get a piece of paper...

[ResidentBiscuit]

All answers are in the 700s :/

[atropos]

I got an answer that's between 700-750

[ResidentBiscuit]

When I re did the problem going at it a different way, I got 726.008. There was an answer of 725.58, so I assumed I was just losing accuracy due to truncating a lot.

Was this similar to what you got?

[atropos]

The answer I got was 725.58m exactly.

[ResidentBiscuit]

Hmm, how did you get there? With pretty much everyone of these types of problems, I tend to be off by roughly .5 to 2.5.

Not sure what I'm doing wrong, mind sharing your process?

[atropos]

Sure thing. For this particular problem, we're given two discrete states.
1) The configuration at T_i = 12^o38'.
2) The configuration at T_f = 50^o11'.

Both of these configurations are right triangles, so the standard formulas can be used.
For the first triangle, tan(12^o38') = 200/x_i.

For the second, tan(50^o11') = 200/x_f.
where x_i and x_f are the initial distance of the boat from the lighthouse base and the final distance, respectively.

The distance the boat travelled between the two states is equal to the difference between x_i and x_f.

EDIT: As a general rule, only computed values should be rounded. Constant expressions should be as accurate as possible.
For example, in this problem the x's are computed values, and each should be rounded to two decimal places (per the instructions). tan(12^o38') and tan(50^o11') are constants and shouldn't be rounded at all.

[ResidentBiscuit]

Ah that was probably my issue. I was converting from minutes to degrees, and losing accuracy there.