Respuesta :
Height of another tree that cast a shadow which is 20ft long is 5 feet approximately
Solution:
Given that tree with a height of 4 ft casts a shadow 15ft long on the ground
Another tree that cast a shadow which is 20ft long
To find: height of another tree
We can solve this by setting up a ratio comparing the height of the tree to the height of the another tree and shadow of the tree to the shadow of the another tree
[tex]\frac{\text {height of tree}}{\text {length of shadow}}[/tex]
Let us assume,
Height of tree = [tex]H_t = 4 feet[/tex]
Length of shadow of tree = [tex]L_t = 15 feet[/tex]
Height of another tree = [tex]H_a[/tex]
Length of shadow of another tree = [tex]L_a = 20 feet[/tex]
Set up a proportion comparing the height of each object to the length of the shadow,
[tex]\frac{\text {height of tree}}{\text {length of shadow of tree}}=\frac{\text { height of another tree }}{\text { length of shadow of another tree }}[/tex]
[tex]\frac{H_{t}}{L_{t}}=\frac{H_{a}}{L_{a}}[/tex]
Substituting the values we get,
[tex]\frac{4}{15} = \frac{H_a}{20}\\\\H_a = \frac{4}{15} \times 20\\\\H_a = 5.33[/tex]
So the height of another tree is 5 feet approximately