Question

A flagpole casts a​ shadow, while at the same​ time, a nearby tree casts a shadow. Use the figure below to find the height n of the flagpole.
9 ft
21
30 ft


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Part 1
The height n of the flagpole is
  
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Answer 1

To determine the height \( n \) of the flagpole using the shadows, we can set up a proportion based on the lengths of the shadows and the heights.

Assuming the lengths of the shadows are given as follows:
- The height of the tree is \( 21 \) ft and its shadow is \( 9 \) ft.
- The height of the flagpole is \( n \) ft, and its shadow is \( 30 \) ft.

The relationship can be set up using the property of similar triangles, which gives us the following proportion:

\[
\frac{\text{Height of tree}}{\text{Shadow of tree}} = \frac{\text{Height of flagpole}}{\text{Shadow of flagpole}}
\]

Substituting the values:

\[
\frac{21}{9} = \frac{n}{30}
\]

Now, we can cross-multiply to solve for \( n \):

\[
21 \times 30 = 9 \times n
\]

This simplifies to:

\[
630 = 9n
\]

Now, divide both sides by \( 9 \):

\[
n = \frac{630}{9}
\]
\[
n = 70
\]

Therefore, the height \( n \) of the flagpole is \( 70 \) ft.