SOLUTION: a weather balloon B lies directly over a 1000-meter airstrip extending from A to C. The angle of elevation from A to B is 55 degrees and from C to B is 37 degrees. Find the distan

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Question 143496: a weather balloon B lies directly over a 1000-meter airstrip extending from A to C. The angle of elevation from A to B is 55 degrees and from C to B is 37 degrees. Find the distance from A to B and from C to B. Please show all work. round to the nearest hundredths.
Answer by Fruglemiester1234(13) (Show Source):
You can put this solution on YOUR website!
Basic Trig problem. For this one all you need to know is the law of sines and you have to make sure to label your drawing correctly

To get the other angle you have to remember that the angles in a triangle add up to 180.

Add 55 and 37 and subtract it from 180.

Then our picture looks like this:

Then we can use the law of sines.
The law of sines equation is:
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In order to use these equations all we need is one angle and its opposite side. Sense we already figured out what our other angle is we can use this formula to calculate our sides.
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We can start by finding either side, its up to you which one you do first. I'll do side c first.
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Our equation would look like this:

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Then we cross multiply:

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Divide both sides by :

Put that in our calculator or look up sine in the back of your text book you end up with:

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You then do the same exact thing with side b:

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cross multiply:

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Divide by

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Plug into calculator or look up sin values and compute manually:

your answers are:

Sorry if these are a little off, I didn't have a scientific calculator on hand so I had to use a solver I found online....