Question 1089555: Points A and B are on opposite sides of a lake. A point C is 81.3 meters from A. The measure of angle BAC is 78.33°, and the measure of angle ACB is determined to be 34.167°. Find the distance between points A and B (to the nearest meter).
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i think you would use the law of sines here.
that law states that a/sin(A) = b/sin(B) = c/sin(C)
a is the side opposite angle A which is equal to CB
b is the side opposite angle B which is equal to AC
c is the side opposite angle C which is equal to AB
angle B is equal to 180 - angle A - angle C
this makes angle B = 67.503 degrees.
by the law of sines, b/sin(B) = c/sin(C)
solve for c to get c = b * sin(C) / sin(B)
this becomes:
c = 81.3 * sin(34.167) / sin(67.503)
this results in c = 49.41948691
c is equal to the length of line segment AB, therefore your solution.
if you round it to the nearest meter, you would get 49.
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