A person that is 5 feet tall casts a shadow 25 feet long. How long is the shadow of a tree that is 15 feet tall?

The person and his shadow make a right triangle as well as the tree and it's shadow. they will be similar right triangles containing angles that are equal. I'm in similar triangles the angles are proportional so a ratio could be used to determine the shadow length. this ratio is:

25/5 = x/15

(Notice that both the height of the person and

the height of the tree height of the tree are on

the bottom because these would be similar

sides and the same for the shadows with both

on top. this could easily have been switched

with the shadows on bottom and heights on

top like:

5/25 = 15/x

however I noticed the 25/5 could easily be

reduced. this eliminated the need for cross

multiplication.)

The 25/5 can be reduced to 5:

5 = x/15

and then multiply both sides by 15 and you get:

x = 75

so the answer is 75 feet long.

this can be checked various ways. using trigonometry we have the opposite and adjacent sides so tangent could be used to find the angle between the shadow and the hypotenuse. this is:

tan (x) = opposite/adjacent

opposite = height

adjacent = shadow

so:

tan (x) = 5/25 for person

tan (x) = 15/75 for tree

these equations both reduce to:

tan (x) = 1/5

And of both equations are the same then the angLee are equal creating similar triangles and a correct answer