Question

a pole that is 3.4 m tall casts a shadow that is 1.54 m long. at the same time, a nearby tower casts a shadow that is 40.25 m long. how tall is the tower? round your answer to the nearest meter.

Explanation:

Step1: Set up proportion

Since the ratio of height to shadow - length is the same for both the pole and the tower, we can set up the proportion $\frac{h_{1}}{s_{1}}=\frac{h_{2}}{s_{2}}$, where $h_{1}$ is the height of the pole, $s_{1}$ is the shadow - length of the pole, $h_{2}$ is the height of the tower, and $s_{2}$ is the shadow - length of the tower. Let $h_{1} = 3.4$ m, $s_{1}=1.54$ m, and $s_{2}=40.25$ m. Then the proportion becomes $\frac{3.4}{1.54}=\frac{h_{2}}{40.25}$.

Step2: Solve for $h_{2}$

Cross - multiply to get $1.54h_{2}=3.4\times40.25$. First, calculate $3.4\times40.25 = 136.85$. Then $h_{2}=\frac{136.85}{1.54}$.

Step3: Calculate the value of $h_{2}$

$h_{2}=\frac{136.85}{1.54}\approx88.8636$ m.

Step4: Round to the nearest meter

Rounding $88.8636$ to the nearest meter gives $89$ m.

Answer:

$89$ m