Question

Tony is 5.75 feet tall. Late one afternoon, his shadow was 8 feet long. At the same time, the shadow of a nearby tree was 32 feet long. Find the height of the tree.

Answer 1

the height of the tree is 23 feet .

Step-by-step explanation:

Here we have , Tony is 5.75 feet tall. Late one afternoon, his shadow was 8 feet long. At the same time, the shadow of a nearby tree was 32 feet long. We need to find Find the height of the tree. Let's find out:

According to question , Tony is 5.75 feet tall. Late one afternoon, his shadow was 8 feet long . Let the angle made between Tony height and his shadow be x . Now , At the same time, the shadow of a nearby tree was 32 feet long. Since the tree is nearby so tree will subtend equal angle of x. Let height of tree be y , So

⇒ $Tanx=\frac{y}{32}$

But , From tony scenario

⇒ $Tanx=\frac{5.75}{8}$

Equating both we get :

⇒ $\frac{y}{32} = \frac{5.75}{8}$

⇒ $y=\frac{5.75(32)}{8}$

⇒ $y=23ft$

Therefore , the height of the tree is 23 feet .