Question

at a certain time of the day a tree casts its shadow 12.5 feet long if the height of the tree is 5 feet find the height of another tree that casts its shadow 20 feet long at the same time​

Answer 1

Answer:

6.5feet.This is the current answer which I got

Answer 2

Answer:

The height of the other tree is 8 feet .

Step-by-step explanation:

Given as :

The length of the shadow caste by one tree = x = 12.5 feet

The height of the one tree = h = 5 feet

Let The angle made by between shadow and ground = Ф

According to question

Tan angle = $\dfrac{\textrm perpendicular}{\textrm base}$

Or, Tan Ф = $\dfrac{x}{h}$

Or,  Tan Ф = $\dfrac{12.5}{5}$

Or, Tan Ф = 2.5          ...........1

Again

At The same time other tree cast shadow

The length of the shadow of other tree = X = 20 feet

Let The height of the other tree = H feet

∵  Both tree make shadow at same time

So, The angle made by both trees are same

∴ Tan Ф = $\dfrac{\textrm perpendicular}{\textrm base}$

Or, 2.5 = $\dfrac{X}{H}$

Or, 2.5 = $\dfrac{20}{H}$

∴ H = $\dfrac{20}{2.5}$

i.e H = 8 feet

So, The height of the other tree = H = 8 feet

Hence, The height of the other tree is 8 feet . Answer