A woodcutter determines the height of a tall tree 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 20 ft tall, the man is 25 ft from the small tree, and his eye level is 5ft above the ground. How tall is the taller tree.

Question

anonymous · Answer

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phi · Answer

can you find "similar triangles" ?

anonymous · Answer

is there one at  the smaller tree with measurements of 25 bottom and 5 to the right and hypotenuse is a ?

phi · Answer

the triangles are from the man's eye over to the short tree,  
and from the man's eye to the tall tree

phi · Answer

you have to adjust some of the numbers.  The first triangle has a leg that is the height of the short tree minus the height of the man's eye.

phi · Answer

here it is with some numbers

phi · Answer

now write a ratio,  vertical leg / bottom leg = vertical leg / bottom leg
or
15/25 = (x-5)/150
now solve for x