Question

A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree. Note that the two triangles are proportional to one another.

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Answer 1

Answer:

30 ft

Step-by-step explanation:

Let the height of the tree be x ft. There are two right triangles:

1. Tree and its shadow are two legs of the first triangle;

2. Man and his shadow are two legs of the second triangle.

A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. This means these two triangle are similar. Similar triangles have proportional sides' lengths. Hence,

$\dfrac{\text{tree}}{\text{tree shadow}}=\dfrac{\text{man}}{\text{man's shadow}}\\ \\\dfrac{x}{24}=\dfrac{5}{4}\\ \\4\cdot x=5\cdot 24\\ \\x=\dfrac{5\cdot 24}{4}=5\cdot 6=30\ ft$

Answer 2

Answer:

30 feet

Step-by-step explanation:

We are given that a tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet.

We are to find the height of the tree.

Using their proportions to compare the height of each object to the length of the shadow.

$\frac{h}{24} =\frac{5}{4}$

$h=\frac{5\times24}{4}$

$h=30$

Therefore, the height of the tree is proportion comparing the height of each object to the length of the shadow 30 feet.