to determine how far apart a boar is from shore, two radar stations 500 feet apart determine the angles out of the boat as shown. Find the distance of the boat from station A.

Answer 1

Draw diagram and recognize that the angle 180-(α+β) is the angle at the boat opposite the 500 feet and alpha and beta are the angles at A and B respectively. The distance from A to the boat is b, the side opposite to beta.

Use sine law: b/sin(β) = 500/sin(180 - (α+β)) = 500/sin(α+β) (using sin of difference of angles formula)

This leaves b = 500 sin(β)/sin(α+β)

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