# Word problem help needed!

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• Feb 3rd 2006, 10:25 PM
sallyann
Word problem help needed!
Height of a tree

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 small tree, and his eye level is 5ft above the ground. How tall is the taller tree?

5ft....................20ft..................talle r tree
25ft 125ft

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!
• Feb 3rd 2006, 11:18 PM
CaptainBlack
Quote:

Originally Posted by sallyann
Height of a tree

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 small tree, and his eye level is 5ft above the ground. How tall is the taller tree?

5ft....................20ft..................talle r tree
25ft 125ft

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!

The triangle from the eye of the wood cutter to the top of the first
tree to a point $5ft$ above the base of the tree is similar to the
triangle from the eye of the wood cutter to the top of the larger
tree to a point $5ft$ above the base of the tree.

The bases of these triangles are $25ft$ and $150ft$ respectivly, so as
they are similar their heights are in the same ratio and the height
of the first triangle is $(20-5)=15ft$ so the height
of the second triangle is:

$15 \times \frac{150}{25}=90ft$.

The second tree is $5ft$ taller than the secon triangle,
so the tree is $95ft$ tall.

RonL
• Feb 6th 2006, 07:31 AM
sallyann
Thank You!!
I Really Appreciate It!