SOLUTION: 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.

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(52921) (Show Source): You can put this solution on YOUR website!
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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).

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On cosine law, see the lessons
- Proof of the Law of Cosines revisited
- Solve triangles using Law of Cosines
in this site.

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