Answer:
[tex]20[/tex] ft
Step-by-step explanation:
We know that the height of the object and the height of the shadow it casts are proportional. Therefore, if we let the length of the tree be [tex]x[/tex], we can set up the following proportion to solve for it:
[tex]\frac{5}{8}=\frac{x}{32}[/tex]
Solving for [tex]x[/tex], we get:
[tex]\frac{5}{8}=\frac{x}{32}[/tex]
[tex]8*x=5*32[/tex] (Cross-Products Property)
[tex]8x=160[/tex] (Simplify)
[tex]\frac{8x}{8}=\frac{160}{8}[/tex] (Divide both sides of the equation by 8 to get rid of [tex]x[/tex]'s coefficient)
[tex]x=20[/tex] (Simplify)
Therefore, the tree is [tex]20[/tex] ft tall. Hope this helps!
