Question

a six foot tall man stands next to a flagpole the man casts a 4 foot shadow and the flag pole casts a 30 foot shadow what is the height of the flag pole

Answer 1

The Solution.

Step 1:

We shall represent the problem in a diagram.

Step 2:

We shall use Similarity Theorem to find the height of the flagpole.

Let H = height of the flagpole.

$\begin{gathered} By\text{ Similarity,} \\ \frac{AB}{AC}=\frac{AD}{AT} \\ \\ \frac{4}{30}=\frac{6}{H} \\ \text{Cross multiplying, we get} \\ 4H=30\times6 \\ 4H=180 \\ \text{Dividing both sides by 4, we get} \\ H=\frac{180}{4}=45\text{ feet} \end{gathered}$

Thus, the correct answer is 45 feet.