Question

A 3-ft stick is perpendicular to the ground. It casts a 5.25-ft shadow. At the same time, a nearby water tower casts a shadow that is 210 ft long. How tall is the water tower?

A. 105 ft
B. 84 ft
C. 3.5 ft
D. 70 ft

Answer 1

The height of the water tower is 120 ft.

Step-by-step explanation:

To solve this problem, we can use similar triangles. We have a 3-ft stick and a 5.25-ft shadow, and a water tower with an unknown height and a 210-ft shadow. The ratio of the stick's height to its shadow is the same as the ratio of the water tower's height to its shadow. We can set up a proportion to find the height of the water tower:

3/5.25 = x/210

Cross multiplying, we get 5.25x = 3 * 210

Dividing both sides by 5.25, we find that x = 3 * 210 / 5.25 = 120 ft.

Therefore, the water tower is 120 ft tall. The correct answer is D. 120 ft.