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a ship is coming into a harbor on an unusually high tide. The ship has to pass under the harbor bridge but the captain doesn't know if the ship will fit. he uses a theodolite to measure the angle at an unknown distance from the bridge and then re-measures the angle when he is 300 meters closer. The first angle measured is 2.3 degrees from sea level and the second angle is 3.3 degrees from sea level. If the ships height is 35metres out of the water, will it fit under the bridge.

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have you tried drawing the triangles?
|dw:1337463129517:dw| tan(3.3) = O/x tan(2.3) = O/(x+300)

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Other answers:

Solve the first equation for x, substitute into the second equation and solve for O.

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