Question

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Answer 1

A person who is 5.5 feet tall stands next to a tree and casts a shadow that is 2 feet long.At the same time, the shadow of the tree casts a shadow that is 8 feet long. how tall is the tree?

Answer 2

we have two triangles here

1 with the two right angld sides = 5.5 and 2 (the base)
other with with one 8 ft long The base)

as the sun makes the same angle with man an dtree these two triangles are similar
and the corresponding sides are in the same ratio

so x / 8 = 5.5 /2 where x is the height of the tree

solving foe x

x = 2x = 5.5* 8
x = 44 /2 = 22

Answer 3

last line but one shld read 2x = 5.5 * 8

Answer 4

A trig solution follows:
TreeHeight =8 Tan[ ArcTan[5.5/2] ] = 22