Question

use the following information and diagram to answer #5–6.
two trees are near one another in a park. one tree stands 108.5 feet
high and casts a shadow that is 31 feet long. the other tree is 42
feet high.

diagram of two right triangles representing trees and their shadows, with heights 108.5 feet and 42 feet, and the first shadow 31 feet

question 1
1 point

how long is the shadow of the shorter tree?
______ feet

Explanation:

Step1: Set up proportion

$\frac{\text{Height of tall tree}}{\text{Length of its shadow}} = \frac{\text{Height of short tree}}{\text{Length of its shadow}}$
Let $x$ = length of shorter tree's shadow.
$\frac{108.5}{31} = \frac{42}{x}$

Step2: Cross-multiply to solve for $x$

$108.5x = 42 \times 31$
$108.5x = 1302$

Step3: Isolate $x$

$x = \frac{1302}{108.5}$
$x = 12$

Answer:

12 feet