Question

a 10ft tall flagple stands next to a tree. the shadow of the flagpole is 17ft and the shadow of the tree is 50ft. what is the height of the tree?

Answer 1

You can solve this problem by writing an equation of ratios and finding the value of the unknown that way:

10 ft 17 ft

---------- * ---------

50 ft x

Then 10x = 850, and so x = 85 feet.

Answer 2

This is a "similar triangle" problem. Set up a ratio comparing the flagpole to the tree as follows and cross multiply to solve for the missing value:

$\frac{flagpole height}{flagpole length}$ = $\frac{tree height}{tree length}$

$\frac{10}{17}$ = $\frac{x}{50}$

(10)(50) = (17)(x)

$\frac{500}{17}$ = x

29.4 ≈ x

Answer: 29.4 ft