Question 1106004: A triangular field is bordered by 18.0m of road, 12.0m of fence and 10.0m of stone wall. Find the angle the road makes with the fence. Answer by ikleyn(52915) (Show Source):
Your angle (I will call it "angle A") is concluded between the sides of 18 m (road) and 12 m (fence).
This angle is opposite to the side of 10 m.
Use the Cosine Law:
10^2 = 18^2 + 12^2 - 2*18*12*cos(A),
which gives cos(A) = = 0.8519.
Then < A = arccos(0.8519) = 0.55 radians = 31.6 degrees (approximately).
