algebra word problem

Question

Suppose you are standing such that a 42-foot tree is directly between you and the sun. If you are standing 100 feet away from the tree and the tree casts a 120-foot shadow, how tall could you be and still be completely in the shadow of the tree?

Answer 1

If you were completely in the shadow of the tree, your shadow would be 20 feet long.

Tree height / shadow length =

My height / my shadow

42 feet / 120 feet = x / 20 feet

Simplify:

(6*7)/(6*20) = x / 20 feet

Multiply both sides by 20 feet:

7/20 = x / 20 feet

x = 7 feet

Since 7/20 is the same ratio as 42/120, we have found the correct answer.

Answer 2

42 foot tree casts a 120 foot shadow

you are 100 feet from the tree and completely in the tree's shadow. opposite the sun

how tall could you be? 7 feet tall

it might help to draw a rough sketch

ignoring the earth's curvature

construct 2 similar right triangles

one with height 42, base 120

2nd with height x, base 120-100=20

x/20 = 42/120= a constant height to base ratio

x = 42/6 = 7 feet tall = your height

you must play basketball? in the NBA?