Question

A tree with a height of 4 ft casts a shadow 15ft long on the ground how tall is another tree that cast a shadow which is 20ft long

Answer 1

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

`\frac{\text {height of tree}}{\text {length of shadow}}`

Let us assume,

Height of tree =
`H_t = 4 feet`

Length of shadow of tree =
`L_t = 15 feet`

Height of another tree =
`H_a`

Length of shadow of another tree =
`L_a = 20 feet`

Set up a proportion comparing the height of each object to the length of the shadow,

`\frac{\text {height of tree}}{\text {length of shadow of tree}}=\frac{\text { height of another tree }}{\text { length of shadow of another tree }}`

`(H_(t))/(L_(t))=(H_(a))/(L_(a))`

Substituting the values we get,

`(4)/(15) = (H_a)/(20)\\\\H_a = (4)/(15) * 20\\\\H_a = 5.33`

So the height of another tree is 5 feet approximately