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.