Question

5. The shadow of a tree extends 25 feet from the top of the tree to the ground. Sarah measures thatthe distance from the base of the tree to the tip of its shadow is 15 feet. How tall is the tree?A. 20 feetB. 25 feetC. 29.2 feetD. 40 feetO

Answer 1

The height of the tree is determined using the properties of similar triangles, forming a right triangle pattern. Given a 3-4-5 triangle pattern with the hypotenuse being 25 feet and one leg being 15 feet, the tree's height is calculated to be 20 feet.

Step-by-step explanation:

To solve the problem of finding the height of the tree when given the shadow length and the distance from the tree to the tip of its shadow, we can use the properties of similar triangles. In this context, the tree and its shadow create a right triangle with the tree's height as one leg and the shadow length as the other leg. The given distances form a 3-4-5 right triangle, where the shadow is 25 feet (hypotenuse), and the distance from the base of the tree to the tip of the shadow is 15 feet (one leg). The height of the tree is the other leg, which corresponds to 20 feet in the 3-4-5 right triangle pattern, so the height of the tree is 20 feet.

Steps to Calculate the Height

1. Recognize the right triangle formed by the tree's height, shadow, and the distance from the tree to the shadow's tip.
2. Apply the Pythagorean Theorem or identify the pattern of a 3-4-5 triangle.
3. Calculate or deduce that the height of the tree must be the missing side, which is 20 feet in this case.

The correct answer is A. 20 feet.

Answer 2

Given :

The shadow of the tree = 25 feet from the top of the tree to the ground

the distance from the base of the tree to tip of its shadow is 15 feet

Let the height of the tree = x

So, 25 , 15 and x are forming a right angle triangle

25 is the hypotenuse of the triangle ,

x and 15 are the legs of the triangle

WE will find x using Pythagorean theorem

So,

`\begin{gathered} x^2+15^2=25^2 \\ x^2=25^2-15^2=625-225=400 \\ x=\sqrt[]{400}=20 \end{gathered}`

So, the height of the tree = 20 feet

The answer is option A. 20 feet