A 5 ft man cast a shadow of 3 ft standing next to a 22ft building. How far is the man standing from the building?
To find the distance between the man and the building, we can use the concept of similar triangles. Let's denote the distance between the man and the building as 'x'.
We have two similar right triangles here: the small triangle formed by the man, his shadow, and the ground, and the larger triangle formed by the building, its shadow, and the ground.
By comparing the corresponding sides of these triangles, we can create a proportion:
(man's height) / (man's shadow length) = (building's height) / (building's shadow length)
Substituting the given values:
5 ft / 3 ft = 22 ft / x
We can cross-multiply and solve for x:
5 ft * x = 3 ft * 22 ft
x = (3 ft * 22 ft) / 5 ft
Simplifying this further:
x = 66 ft / 5 ft
x = 13.2 ft
Therefore, the man is standing approximately 13.2 feet away from the building.