A person 6 ft. tall is standing near a street light so that he is 4/10 of the distance form the pole to the tip of his shadows How high above the ground is the light bulb?
If the distance from the pole to the tip of the shadow is x, then the height h of the pole can be found using
h/x = 6/.6x
h = 10 ft
To solve this problem, we'll need to use proportions. Let's call the height of the person h and the height of the street light x.
According to the problem, the person is 6 ft. tall and standing in such a way that he is 4/10 (or 2/5) of the distance between the pole and the tip of his shadow. This means the distance between the person and the pole is 2/5 of the distance between the person and the tip of his shadow.
Let's assume the distance between the person and the pole is d. Since the person is 4/10 of the distance from the pole to the tip of his shadow, the remaining distance from the person to the tip of his shadow is (1 - 4/10) = 6/10 (or 3/5) of d.
So, the total distance from the pole to the tip of the person's shadow is d + (3/5)d = (8/5)d.
Now, we can set up a proportion:
(h / x) = (d / (8/5)d)
We cross-multiply and simplify the equation:
5h = 8x
Therefore, the height of the light bulb (x) is equal to (5/8) times the height of the person (h).
Given that the person's height is 6 ft., we can substitute the value into the equation:
x = (5/8) * 6
x = 3.75 ft.
Therefore, the light bulb is 3.75 ft. above the ground.