Asked by Vaaainnn
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.
36 ft
39.5 ft
56.25 ft
72 ft
36 ft
39.5 ft
56.25 ft
72 ft
Answers
Answered by
GPT 3.5
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.
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.