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,

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

$\frac{H_{t}}{L_{t}}=\frac{H_{a}}{L_{a}}$

Substituting the values we get,

$\frac{4}{15} = \frac{H_a}{20}\\\\H_a = \frac{4}{15} \times 20\\\\H_a = 5.33$

So the height of another tree is 5 feet approximately