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#### daveyc3000

##### New member

- Dec 29, 2018

- 2

Answer: 55 m.

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- Dec 29, 2018

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Answer: 55 m.

- Aug 30, 2012

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As Dr, Peterson asked you on FMH: "What have you tried so far?" (Aside from posting the problem on just about any Math forum.)

-Dan

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- Feb 5, 2013

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... and if you're stuck doing that try making a diagram if you haven't done so already.

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- Dec 29, 2018

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Nothing but I have found the answer and now understand the problem

Thanks !

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I've given this thread a useful title, and now, let's make the content useful to others by actually showing the work.Nothing but I have found the answer and now understand the problem

Thanks !

We are not told where along the bottom of the gorge Jon is, so let's let his distance from the taller side be \(x\). All measures are in meters.

And then we may state:

\(\displaystyle \tan\left(65^{\circ}\right)=\frac{72}{x}\)

\(\displaystyle \tan\left(35^{\circ}\right)=\frac{15}{w-x}\)

The second equation implies:

\(\displaystyle w=15\cot\left(35^{\circ}\right)+x\)

The first equation implies:

\(\displaystyle x=72\cot\left(65^{\circ}\right)\)

Hence:

\(\displaystyle w=15\cot\left(35^{\circ}\right)+72\cot\left(65^{\circ}\right)\approx54.99637148829162\)