Question

a 70 - ft tree casts a 10 - ft shadow at the same time a nearby cell phone tower casts a 122 - ft shadow. how tall is the cell phone tower?
the cell phone towers height is (square) ft. (simplify your answer.)

Explanation:

Step1: Set up proportion

Since the ratio of object height to shadow length is the same for both the pole and the cell - phone tower at the same time, we can set up a proportion. Let the height of the cell - phone tower be $h$. The proportion is $\frac{height\ of\ pole}{shadow\ of\ pole}=\frac{height\ of\ tower}{shadow\ of\ tower}$. Given the pole is 70 ft high with a 10 - ft shadow and the tower has a 122 - ft shadow, so $\frac{70}{10}=\frac{h}{122}$.

Step2: Solve for $h$

Cross - multiply the proportion: $10h = 70\times122$. Then $h=\frac{70\times122}{10}$. Calculate $70\times122 = 8540$, and $\frac{8540}{10}=854$.

Answer:

854