Question

A woman wants to measure the height of a nearby tower. She places a 10 ft pole in the shadow of the tower so that the shadow of the pole is exactly covered by the shadow of the tower. The total length of the tower's shadow is 190 ft, and the pole casts a shadow that is 3.25 ft long. How tall is the tower? Round your answer to the nearest foot. (The figure is not drawn to scale.)

Answer 1

Explanation:

Let's denote the height of the tower as "h" feet.

According to the given information, the length of the pole's shadow is 3.25 ft, and the total length of the tower's shadow (including the shadow of the pole) is 190 ft.

We can set up a proportion using the similar triangles formed by the tower, its shadow, the pole, and its shadow:

height of the tower / length of the tower's shadow = height of the pole / length of the pole's shadow

h / 190 = 10 / 3.25

Cross-multiplying:

h * 3.25 = 10 * 190

h * 3.25 = 1900

Dividing both sides by 3.25:

h = 1900 / 3.25

h ≈ 584.62

Rounding to the nearest foot, the height of the tower is approximately 585 feet.