A ship is just offshore of New York City. A sighting is taken of the statue of Liberty, which is about 305 feet tall. If the angle of elevation to the top of the statue is 20 degrees, how far is the ship from the statue?

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- Nov 13th 2008, 02:52 AM #1

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- Nov 13th 2008, 05:06 AM #2

- Nov 13th 2008, 06:40 AM #3

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- Nov 13th 2008, 10:25 PM #4

- Nov 14th 2008, 09:47 AM #5

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No need to introduce cotangent here. Most calculators don't have a COT key, so why use the reciprocal when good ole TAN will do nicely?

$\displaystyle \tan20^{\circ}=\frac{305}{x}$

$\displaystyle x \tan20^{\circ}=305$

$\displaystyle x=\frac{305}{\tan 20^{\circ}}$

$\displaystyle x\approx 837.98$ feet from the statue.

- Nov 14th 2008, 01:02 PM #6

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- Nov 14th 2008, 01:03 PM #7

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