Finally! Mathew sees a fish, but needs to know how far to let his fishing line down to get to the fish!
We need to use the Law of cosines! c^2=a^2+b^2-2ab*cos(C).
The next day, Matthew and his sister, Jessica go to the park together. But sad news! Jessica got her kite stuck in a tree. :(
Matthew John X?? 17 feet 28 feet 114° Teddy
In our case, X^2 = 28^2+17^2-2(28)(17)cos(114).
Matthew knows what to do! He figures out that they and the kite are all at 60° angles, and Jessica is 30 feet from the kite, because that is how long the string is. Now Matthew wants to know how far from Jessica he is!
We need to use the Law of Sines!Sin(A) Sin(B)------ = ------a b
Later that day, Matthew was playing catch with two of his friends, before dinner. After a while of playing, the boys want to find out how far apart Matthew and John are, without simply measuring.
With that equation, X^2=1460.21 andX=38.21
They know that Teddy makes a 114° angle with both of them, Matthew is 17 feet away from Teddy, and John is 28 feet from Teddy.