For the traffic signal, you know both the height and the shadow length. What ratio can you form from these two measurements?

If the height-to-shadow ratio is the same for both objects, how can you use the ratio from the traffic signal to write an equation involving the hydrant’s unknown height and its 4-foot shadow?

Once you have an equation of the form $\frac{24}{32} = \frac{h}{4}$, solve for $h$ using either cross-multiplication or by simplifying the fraction $24/32$ first.

In Desmos, type 24/32 and note the simplified decimal value; this is the common ratio of height to shadow for both objects.

Next, type (24/32)*4 (the ratio multiplied by the hydrant’s 4-foot shadow). The numerical output Desmos gives for this expression is the hydrant’s height in feet.

Both the traffic signal and the fire hydrant stand vertically and cast shadows on level ground at the same time of day. The sun’s rays are effectively parallel, so the triangles formed by each object and its shadow are similar right triangles. That means their height-to-shadow ratios are equal.

Let $h$ be the height of the fire hydrant in feet.

For the traffic signal:

• Height: $24$
• Shadow: $32$

For the hydrant:

• Height: $h$
• Shadow: $4$

Since the triangles are similar, set up the proportion:

Simplify the left side:

So we have:

Because the denominators are the same, the numerators must be equal, so $h = 3$.

Therefore, the height of the fire hydrant is 3 feet, which corresponds to answer choice B) 3.