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 .

Answer 2

The ratio of the heights of Tony and the tree to the lengths of their shadow are equal.

The height of the tree is 23 feet

Reasons:

Tony's height = 5.75 feet

The length of his shadow = 8 feet

The length of the shadow of the nearby tree = 32 feet

Required:

The height of the tree

Solution:

Using common ratios formed by the similar triangles formed by the

shadows cast by the tree and Tony, we have;

$\displaystyle \frac{Tony's \ height}{Length \ of \ Tony's \ shadow} = \mathbf{\frac{Height \ of \ the \ tree}{Length \ of \ the \ tree's \ shadow}}$

Therefore, we have;

$\displaystyle \frac{5.75 \, feet}{8 \, feet} = \frac{Height \ of \ the \ tree}{32 \, feet}$

Which gives;

$\displaystyle Height \ of \ the \ tree = \frac{5.75 \, feet \times 32 \, feet}{8 \, feet} = \mathbf{23 \, feet}$

The height of the tree = 23 feet

Learn more about similar triangles here:

https://brainly.com/question/6198345