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Answer:
596.0 ft
Step-by-step explanation:
The relationship between the two legs of a right triangle and an acute angle is ...
Tan = Opposite/Adjacent
The height (h) of the lighthouse is the side opposite the angles of elevation. If d is the distance between A and B, we can write two tangent relations:
tan(14°) = h/770
tan(8°) = h/(770 +d)
Equating expressions for h gives ...
770·tan(14°) = (770 +d)·tan(8°)
770(tan(14°) -tan(8°)) = d·tan(8°) . . . . subtract 770·tan(8°)
d = 770·(tan(14°)/tan(8°) -1) . . . . . divide by the coefficient of d
d ≈ 770·(1.7740609 -1) = 596.03
The distance from point A to point B is about 596.0 feet.
