A person 6ft tall is standing near a st. light so that he is 4/10 of the distance from the pole to the tip of?

Question

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

solve this with similar triangles:

Triangle 1
Tip of shadow to base of pole, pole from ground to bulb, bulb to tip of shadow.

Triangel 2
Tip of shadow to person's feet, height of person, top of person's head to tip of shadow

Similar triangles says that:

(person's height)/(pole height) = (person's shadow length)/(distance from tip of shadow to base of Pole)

we know that (person's shadow length)/(distance from tip of shadow to base of Pole) = (6/10)/(10/10) = 6/10

then (person's height)/(pole height) = 6/10
since the person is 6 ft tall, we get 6ft/(pole height) = 6/10...
solving for pole height.. we get 10 ft.

use the same method to calculate similar triangles for the person's head being 5 feet from the light bulb (only this is on the hypotenuse of the triangles).

First.. we know that the light is 10 ft above the ground.. and the person's head is 6 feet, with the head 5 ft from the light.. so.. make a triangle:
hypotenuse = 5 ft
right leg = 10-6 = 4 ft
bottom leg = X

x^2 + 4^2 = 5^2 ==> x^2 + 16 = 25 ==> x^2 = 9 ==> x = 3

now... 3 = 4/10d (where d = distance of shadow tip from pole)
or d = 3 * (10/4) = 30/4 = 15/2 so the pole is 7 1/2 ft from the tip of the shadow and the shadow starts at 3 ft from the pole.. so

7 1/2 - 3 = 4 1/2ft for the length of the shadow

I'll let you check the work for mistakes

Answer 2

let the distance of the tip of the shadow from the pole be x
distance of the man from the pole=4/10x and the length of the shadow=6/10x
let the length of the pole be y
the portion of the pole above the man's head =y-6
using similar triangles y-6/y=(4/10x)/x
solving (y-6)=4/10y=>(6/10)y=6 so y=10
therefore the length of the pole above the man's head=4'
it is given the persons head is exactly 5' from the light bulb
so using the Pythagorean triad 5,4,3 distance of the man from the pole=3'
but that distance is 4/10 x therefore 4/10x=3' or x=7.5'
length of the shadow 7.5-3=4.5'
answer the person is 3' from the pole and the length of the shadow is 4.5'

Answer 3

ITS 43628