Question

1. at the same time that an 11 - inch - tall weathervane casts a 16 - inch shadow, a nearby lightning rod casts a 28 - inch shadow. how tall is the lightning rod?

Explanation:

Step1: Set up proportion

Let the height of the lightning - rod be $x$ inches. Since the ratio of the height of an object to its shadow length is the same for both the weathervane and the lightning - rod at the same time, we can set up the proportion $\frac{11}{16}=\frac{x}{28}$.

Step2: Cross - multiply

Cross - multiplying gives us $16x = 11\times28$.

Step3: Calculate the right - hand side

$11\times28=308$, so $16x = 308$.

Step4: Solve for $x$

$x=\frac{308}{16}=\frac{77}{4}=19.25$ inches.

Answer:

$19.25$ inches