SOLUTION: Points A and B are on opposite sides of a river. To find the distance between the points, a third point C is located on the same side of the river as point A. The distance between

Algebra ->  Trigonometry-basics -> SOLUTION: Points A and B are on opposite sides of a river. To find the distance between the points, a third point C is located on the same side of the river as point A. The distance between       Log On


   

Question 813263: Points A and B are on opposite sides of a river. To find the distance between the points, a third point C is located on the same side of the river as point A. The distance between A and C is 43 feet, ∠ACB is determined to be 42° and ∠BAC is 105°. Find the distance between A and B. (Round your answer to one decimal place.)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
It might help if you draw a diagram:
  1. Draw a triangle and label the vertices A, B and C.
  2. Label side AC as 43 feet.
  3. Label angle BAC as 105 degrees.
  4. Label angle BCA as 42 degrees.
  5. Label side BC as x (since that is what we are looking to find).
Probably the easiet way to find x is to use the Law of Sines. This will require that we know what the angle opposite side AC is. Using the fact that the three angles add up to 180 we should be able to use the other two angles to find the third one. The third angle, ABC, is 33 degrees.

Now we are ready to use the Law of Sines:
sin%2833%29%2F43+=+sin%2842%29%2Fx
Cross-multiplying we get:
x%2Asin%2833%29+=+43%2Asin%2842%29
Divide by sin(33):
x+=+%2843%2Asin%2842%29%29%2Fsin%2833%29
I'll leave it up to you and your calculator to simplify the right side.