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How far has the ship travelled using Trig?
A ship is sailing due North. At a certain point the bearing of a lighthouse that is 12 miles away is found to be 39 degrees East of due North. Later the bearing is determined to be 44 degrees East of due North. How far, to the nearest tenth of a mile, has the ship traveled?
here is what i did. let me know if i did it right, and if not, then what should i had done to solve it.
tan(39) = 12/x
x1 = 12/tan(39)
x2 = 12/tan(44)
x1 + x2 = (12/tan(39)) + (12/tan(44)) = 27.2
1 Answer
- L. E. GantLv 71 decade agoFavorite Answer
Draw yourself a diagram, and you will see why this is wrong. Often, when dealing with trigonometry, you can get a better idea of what the answer will look like if you draw a diagram first.
Let L be the position of the lighthouse.
Let A be the point where the ship's first angle measurement takes place.
Let B be the point where the second reading was taken.
Then AL = 12, angle BAL = 39 degrees and angle ABL = 180 - 44 = 136 degrees. So, angle ALB = 180 - 39 - 136 = 5 degrees
From the sine relationship:
AL/sin(136) = AB/sin(5) = BL/sin(39)
[we'd use the last one if we wanted to find how far the ship was from the lighthouse at the second reading.]
AB = AL*sin(5)/sin(136) = 12 * sin(5) / sin(44)
Look up the sin values and do the calculation (about 1.5 miles)
