SOLUTION: You attempt to set off in a sail boat for an island that is 8 km away from the dock. After having traveled a distance of 7.2 km in a straight line, you discover that you are 10 deg

Algebra ->  Trigonometry-basics -> SOLUTION: You attempt to set off in a sail boat for an island that is 8 km away from the dock. After having traveled a distance of 7.2 km in a straight line, you discover that you are 10 deg      Log On


   



Question 834934: You attempt to set off in a sail boat for an island that is 8 km away from the dock. After having traveled a distance of 7.2 km in a straight line, you discover that you are 10 degrees off course. How far are you from the island at that point?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This is a triangle, the departure point is at an angle 10 degrees. One side of this angle is 7.2 km, and the other side of this angle is 8 km. The last side of this triangle is how far you are from the other end point of the 8 km. side.

Draw this triangle to see more comfortably.

Law of Cosines.
How far you are, that unknown side, d.
7.2%5E2%2B8%5E2-2%287.2%29%288%29cos%2810%29=d%5E2
highlight%28d=sqrt%287.2%5E2%2B8%5E2-2%287.2%29%288%29cos%2810%29%29%29