Question

Clare, whose eyes are 10 ft. from the ground, finds her line of sight in line with the top, P, of a flagpole and the top, B, of a building. She knows that the pole is 50 ft. tall, her feet are 20 ft. from the base of the pole, and the pole is 100 ft. from the base of the building. What is the height of the building? Don't forget units.

Answer 1

Using similar triangles, we find that the height of the building is 250 feet by setting the ratio of the differences in height to distances equal for Clare's line of sight to the flagpole and the building.

Step-by-step explanation:

We can solve this problem by using similar triangles. Clare's line of sight to the top of the flagpole and the top of the building forms two similar triangles.

The vertical height of Clare's eye level above the ground is 10 feet, and the flagpole's height is 50 feet.

The distance from Clare's feet to the flagpole is 20 feet, and the distance from the flagpole to the building is 100 feet.

Let's label the height of the building as H. Since the triangles formed by Clare's line of sight are similar, the ratios of their corresponding sides are equal:

[(Height of flagpole - Clare's eye level) / Distance from Clare to flagpole] = [(Height of building - Clare's eye level) / (Distance from Clare to flagpole + Distance from flagpole to building)]

Substituting the known values:

[(50 ft - 10 ft) / 20 ft] = [(H - 10 ft) / (20 ft + 100 ft)]

Solving for H:

(40 ft / 20 ft) = (H - 10 ft) / 120 ft

2 = (H - 10 ft) / 120 ft

240 ft = H - 10 ft

H = 250 ft

Therefore, the height of the building is 250 feet.