Question

a pole that is 2.8 m tall casts a shadow that is 1.79 m long. at the same time, a nearby building casts a shadow that is 45.25 m long. how tall is the building? 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 building, we can set up the proportion $\frac{h_{pole}}{s_{pole}}=\frac{h_{building}}{s_{building}}$, where $h_{pole}$ is the height of the pole, $s_{pole}$ is the length of the pole's shadow, $h_{building}$ is the height of the building, and $s_{building}$ is the length of the building's shadow. Let $h_{pole} = 2.8$ m, $s_{pole}=1.79$ m, and $s_{building}=45.25$ m. Then $\frac{2.8}{1.79}=\frac{h_{building}}{45.25}$.

Step2: Solve for $h_{building}$

Cross - multiply to get $1.79\times h_{building}=2.8\times45.25$. Then $h_{building}=\frac{2.8\times45.25}{1.79}$. First, calculate $2.8\times45.25 = 126.7$. Then $h_{building}=\frac{126.7}{1.79}\approx70.89$.

Step3: Round to the nearest meter

Rounding $70.89$ to the nearest meter gives $71$ m.

Answer:

71