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Similar Triangles: Application/Tree Clearance

GEOM-VYDXEH

Mr. Branch works for the Geometree Logging Company, and he is pondering if the tree he is logging will clear a nearby power line in the easement when it falls. He recalls word problems dealing with similar triangles from his geometry class that dealt with shadows and trees. "When am I ever going to use this?" has surfaced!

After aligning his shadow with the shadow of the tree, he sketches the diagram shown above to aid in finding the height of the tree.

If the power line is $90$ feet due west of the tree and the tree falls due west, find the projected feet of clearance the top of the fallen tree will have from the power line OR find the projected feet the top of the tree will land beyond the power line, bringing down the line.

A

$23.44\text { feet clearance}$

B

$29.35\text { feet clearance}$

C

$60.65\text { feet clearance}$

D

$66.56\text { feet clearance}$

E

$708.75\text { feet beyond the power line}$