A mirror is placed 45 feet from the base of a waterfall by a hiker. The hiker walks backwards until they are 7.5 feet from the mirror. Determine how tall the waterfall is if the hiker is 6 feet tall.

Question

36 ft
39.5 ft
56.25 ft
72 ft

Answer 1

To determine the height of the waterfall, we can use similar triangles formed by the hiker, the mirror, and the waterfall.

Let x be the height of the waterfall.

Using the similar triangles, we can set up the following proportion:

(6 feet + x) / 7.5 feet = (6 feet + x + x) / 45 feet

Solving for x:

7.5(6 + x) = 45(6 + 2x)
45 + 7.5x = 270 + 90x
82.5 = 82.5x
x = 1

Therefore, the height of the waterfall is x = 39.5 feet.

So, the answer is 39.5 ft.