Question:

Trigonmetry! Finding the distance of a ship from shore?

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HELP!! Can't seem to figure out this problem! Thanks..

A person in a small boat, offshore from a vertical cliff known to be 100 feet in height, takes a sighting of the top of the cliff. If the angle of elevation is found to be 30 degrees, how far offshore is the ship?

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  1. As the distance s are small, we will ignore Earth's curvature.

    Tan 30 = 1/sqrt3

    = 100'/distance

    Distance = 100(sqrt3) = 173.20 feet


  2. tan 30 / 1 = 100 / distance

    Cross multiply

    100 * 1

    ---------- = 173.2 feet

    tan 30

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