Question

a bench is located where the shadows casted by a 16-foot tall flagpole and a 40-foot tall tree meet. if the bench is 18 feet from the flagpole, find the distance from the flagpole to the tree.

Explanation:

Step1: Set up proportion for flagpole

Let $x$ = length of flagpole's shadow from base to bench.
The height-to-shadow ratio is equal:
$\frac{16}{x} = \frac{40}{d - x}$
Here, $d$ = total distance between flagpole and tree, and the tree's shadow length from its base to bench is $d - 18$? Correct correction: Bench is 18ft from flagpole, so flagpole shadow to bench is 18ft. Let $y$ = distance from bench to tree.
$\frac{16}{18} = \frac{40}{y}$

Step2: Solve for $y$

Cross-multiply to isolate $y$:
$16y = 40 \times 18$
$y = \frac{40 \times 18}{16}$
$y = \frac{720}{16} = 45$

Step3: Calculate total distance

Add flagpole-to-bench and bench-to-tree distances:
$d = 18 + 45$

Answer:

63 feet