Peter needs to find the distance across the pond shown in the diagram. he starts from point c and walks 200 meters to point b. then he turns 105 degrees and walks 180 meters to reach point a at the other side of the pond. the approximate distance across the pond is meters.

Peter walks into 3 different points. If you make a diagram of the direction, you can see that he will form a triangle with a=200, b= 180m, and cos c= cos 180-105= cos 75.
Using law of cosine, the length of C would be:

c^2= a^2 + b^2 - 2ab cos c
c^2= 200^2 + 180^2 - 2(200)(180) cos 75
c^2= 40,000+ 32,400 - 18,645
c^2= 53765
c= 231.87m

Looks pretty good to me!

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.