a person 6 ft. tall s standing near a street light so that he is 4/10 of the distance from the pole to the tip of his shadow. How high above the ground is the light bulb? if the person's head is exactly 5ft from the light bulb. how far is the person from the pole and how long is the shadow?

Answer 1

as usual, draw a diagram.
If the light is at height h, and the person is standing at a distance of 4x from the pole, then

h/10x = 6/6x
h/10 = 6/6
h=10

So, the light is 10 feet up.

Now, if the person's head is 5' from the light,

(4x)^2 + (10-6)^2 = 5^2
(4x)^2 + 4^2 = 5^2

We all know of the 3-4-5 right triangle, so 4x=3

So, 6x = 4.5, and that is the length of the shadow.