How high is a tree that casts a 21 -ft shadow at the same time a 5 -ft post casts a shadow which is 10 -ft long?
The trees height is ft.
(Round to the nearest tenth, if necessary.)

Question

How high is a tree that casts a 21 -ft shadow at the same time a 5 -ft post casts a shadow which is 10 -ft long? The trees height is $$ \square $$ ft. (Round to the nearest tenth, if necessary.)

UpStudy AI · Accepted Answer

We set up a proportion using similar triangles. The ratio of the post's height to its shadow length is the same as the ratio of the tree's height to its shadow length. Let $$ h $$ be the height of the tree. Then:

$$
\frac{h}{21} = \frac{5}{10}
$$

Simplify the right-hand side:

$$
\frac{5}{10} = \frac{1}{2}
$$

Now, solve for $$ h $$ by multiplying both sides of the equation by 21:

$$
h = 21 \times \frac{1}{2} = 10.5
$$

The tree's height is $$ 10.5 $$ ft.
The tree is 10.5 feet tall.

How high is a tree that casts a 21 -ft shadow at the same time a 5 -ft post casts a shadow which is 10 -ft long?
The trees height is ft.
(Round to the nearest tenth, if necessary.)

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How high is a tree that casts a 21 -ft shadow at the same time a 5 -ft post casts a shadow which is 10 -ft long? The trees height is ft. (Round to the nearest tenth, if necessary.)

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Latest Geometry Questions

How high is a tree that casts a 21 -ft shadow at the same time a 5 -ft post casts a shadow which is 10 -ft long?
The trees height is ft.
(Round to the nearest tenth, if necessary.)