SOLUTION: Villages A, B, C, D are such that B is 4 km due east of A, C is 3 km due south of B and D is 4 km S50°W from C. Calculate the distance and bearing of A from D.

Question 1163292: Villages A, B, C, D are such that B is 4 km due east of A, C is 3 km due south of B and D is 4 km S50°W from C. Calculate the distance and bearing of A from D.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Villages A, B, C, D are such that B is 4 km due east of A, C is 3 km due south of B and D is 4 km S50°W from C. Calculate the distance and bearing of A from D.
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AC = sqrt(3^2 + 4^2) = 5 km
angle ACB = atan(3/5) =~ 30.96 degs
angle BCD = 130 - ACB =~ 99.04 degs
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You have 2 sides and the included angle, use the Cosine Law to find AD
Then use the Law of Sines to find the bearing
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Another way to look at it, albeit with nastier arithmetic. All in all, Alan's solution is better.

.

John

My calculator said it, I believe it, that settles it

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