Question

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.

Answer 1

The correct answer is

232

:)

Answer 2

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