Question

a pole that is 2.5 m tall casts a shadow that is 1.15 m long. at the same time, a nearby tower casts a shadow that is 46.75 m long. how tall is the tower? round your answer to the nearest meter.

Explanation:

Step1: Set up proportion

Since the ratio of object height to shadow length is the same for both the pole and the tower, we can set up the proportion $\frac{height_{pole}}{shadow_{pole}}=\frac{height_{tower}}{shadow_{tower}}$. Let the height of the tower be $x$. So, $\frac{2.5}{1.15}=\frac{x}{46.75}$.

Step2: Cross - multiply

Cross - multiplying gives us $1.15x = 2.5\times46.75$.

Step3: Calculate the right - hand side

$2.5\times46.75 = 116.875$. So, $1.15x=116.875$.

Step4: Solve for $x$

$x=\frac{116.875}{1.15}=101.630435$.

Step5: Round to the nearest meter

Rounding $101.630435$ to the nearest meter gives $102$.

Answer:

$102$