SOLUTION: 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

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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