# math

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suppose that we are standing on a bridge 30 feet above a river watching a log (piece of wood) floating toward we. If the angle with the horizontal to the front of the log is 16.7 degree and angle with horizontal to the back of the log is 14 degree, how long is the log?

• math -

if the front of the log is x feet from the bridge, and y is the length of the log, then

30/x = tan 16.7°
30/(x+y) = tan 14°

eliminate x:

30/tan 16.7° = 30/tan 14° - y
Now solve for y:

y = 30(cot 14° - cot 16.7°)

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