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

30 feet

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.

`(h)/(24) =(5)/(4)`

`h=(5*24)/(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.

Answer 2

30 ft

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,

`\frac{\text{tree}}{\text{tree shadow}}=\frac{\text{man}}{\text{man's shadow}}\\ \\(x)/(24)=(5)/(4)\\ \\4\cdot x=5\cdot 24\\ \\x=(5\cdot 24)/(4)=5\cdot 6=30\ ft`