The Bridge to Terabithia
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 m closer. The first angle measured is from sea level and the second angle is from sea level. If the ships height is m out of the water, will it fit under the bridge?
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1 solution
Height of bridge = y meters Initial distance from bridge = x + 300 meters Second distance from bridge = 300 meters
First measurement tan(2.3) = y/(300 + x) or 0.04 = y/(300 + x) or 12 + 0.04x = y --(1)
Second measurement tan(3.3) = y /x 0.06 = y/x or y = 0.06x --(2)
Substitute the value of y from eq(2) in eq(1) 12 + 0.04x = 0.06x or 0.02x = 12 or x = 600
Therefore y = 0.06*600 = 36 meters = height of the bridge
So height of the bridge is greater than height of the ship, which is 35 meters.
So the ship will fit.
(P.S. I am doing this late in the night so I was too lazy to add LaTeX to the solution! Sry... Could someone please help me to convert this to LaTeX?)