Solving triangles with laws of sine and cosine.

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Hollis

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Nov 19, 2007
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The word problem is this:

A lighthouse is sighted from two points, A and B, directly west of the lighthouse and on the same horizontal plane with it's base C. At A the angle of elevation of D, the top of the lighthouse is 13degrees 30minutes and at B the angle is 31degrees 45minutes. If AB is 1156 feet, find the height of the lighthouse to the nearest foot.

I have it drawn and the angles in the right places. I've gone as far as solving all the angles for one of the triangles (ABD), but it's not the one with the side I'm solving for. Basically, I just need to know how to get to where I'm going. I don't know how to solve for CD with the given information, and the things I have solved for.
 
What do you mean by "solving the angles"? How did you do that?
Asking because there is really no solving, as you can get ALL the angles by simple default values.
Did you realise that the angle at C = 90 degrees?

What did you get for triangle ABD: 13.5 (given), 18.25 and 148.25 ?
If so, look up the Law of Sines: you'll be able to calculate BD.
Then you'll be left with right triangle BCD, you'll know its angles plus you'll have the hypotenuse BD: piece of cake!
 
I actually figured it out before hand, but thanks.
And I suppose that solving was a poor choice of wording.
I just needed help, I'm not stupid. =]
 
Hollis said:
I actually figured it out before hand, but thanks.
And I suppose that solving was a poor choice of wording.
I just needed help, I'm not stupid. =]
Click to expand...
Pipe down, Hollis.
I was simply trying to let you know IN CASE you were doing a lot of work for nothing.
 
I wouldn't know how to do it if I were actually solving
the angles. But, thanks.
 
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