Analytic Geometry: How high is the peack above the pool?

[ZETS]

I've got a question here, conerning analytic geometry. I'll appreciate if anyone could help me.

A backpacker 6 ft tall sees the peak of a mountain reflected in a small calm pool. The pool is 2 miles from the peak, according to a map. If the backpacker is 30 ft from the point of reflection in the pool, how high is the peak above the level of the pool?

Thanks in advance.

 

[soroban]

Re: Analytic Geometry

Hello, ZETS!

I wouldn't call this "analytic geometry".
And did you make a sketch?

A backpacker 6 ft tall sees the peak of a mountain reflected in a small calm pool.
The pool is 2 miles from the peak, according to a map.
If the backpacker is 30 ft from the point of reflection in the pool,
how high is the peak above the level of the pool?

                                    *
                                  / |
                                /   |
                              /     |
                            /       |
                          /         |
                        /           | h
      *               /             |
      | \           /               |
    6 |   \       /                 |
      |     \   /                   |
      + - - - * - - - - - - - - - - +
         30           10,560

You have similar right triangles.

Can you find \(\displaystyle h\) ?

 

[ZETS]

No, I didn't make anything and I can't find h, because sadly, I have almost no idea what's my question about....

 

[jonboy]

No, I didn't make anything and I can't find h, because sadly, I have almost no idea what's my question about....

Set up a proportion:

\(\displaystyle \L \;\frac{6}{30}\,=\,\frac{h}{10,560}\)

Solve for \(\displaystyle h\)