Word Problem HELP!!!! PLEASE!!

[pochoa]

Can anyone help with this?

A woodcutter determines the height of a tall tree by first measuring a smaller one 125ft away, then moving so that his eyes are in line of sight along the tops of the trees, and measuring how far he is standing from the small tree (see figure). Suppose the small tree is 20ft tall, the man is 25ft from the tall tree, and his eye level is 5ft above the ground. How tall is the taller tree?


I got 30ft, but I dont think it is right , here is what I did:

(h/150)(5/25) = 750/25 = 30

Any help would be greatly appreciated ! thanks!

 

[stapel]

If he's twenty-five feet from the tall tree and the small tree is 125 feet from the tall tree, then there is no way to line up the trees so their tops align. You'd have to be standing closer to the small tree in order to do that.

Also, what was your reasoning for your solution? Please reply with specifics.

Thank you.

Eliz.

 

[soroban]

Hello, pochoa!

A woodcutter determines the height of a tall tree by first measuring a smaller one 125 ft away,
then moving so that his eyes are in line of sight along the tops of the trees,
and measuring how far he is standing from the small tree.
Suppose the small tree is 20ft tall, the man is 25ft from the tall tree, \(\displaystyle \;\) you mean small tree!
and his eye level is 5ft above the ground. How tall is the taller tree?

                              *F
                           *  |
                     D  *     |
                     *        |
               B  *  |        |h
               *     |20      |
            *  |5    |        |
         *     |     |        |
      *--------+-----+--------+ 
      A   x    C 25  E  125   G

We have three similar right triangles: \(\displaystyle \,\Delta ABC\,\sim\,\Delta ADE\,\sim\,\Delta AFG\)
\(\displaystyle \;\;\)Hence, their sides are proportional.

The ratios \(\displaystyle \frac{\text{height}}{\text{base}}\) are equal.

We have: \(\displaystyle \L\,\frac{5}{x}\;=\;\frac{20}{x\,+\,25}\;=\;\frac{h}{x\,+\,150}\)


From the first two: \(\displaystyle \L\,\frac{5}{x}\:=\:\frac{20}{x\,+\,25}\;\;\Rightarrow\;\;x\,=\,\frac{25}{3}\;\) [1]

From the first and last: \(\displaystyle \L\,\frac{5}{x}\:=\:\frac{h}{x\,+\,150}\;\;\Rightarrow\;\;h\:=\:\frac{5(x\,+\,150)}{x}\;\) [2]


Substitute [1] into [2]: \(\displaystyle \L\:h\;=\;\frac{5\left(\frac{25}{3}\,+\,150\right)}{\frac{25}{3}}\;=\;95\)

 

[pochoa]

Thanks so much for your help!

I see I set up the problem completely!

thanks again!

 

[pochoa]

completly WRONG that is!

Thanks!