Question

a 6 foot tall person is standing x feet away from a 10 ft lamppost. What is the distance d from the base of the lamppost to the end of the persons shadow, expressed as a function of x?

Answer 1

d =
`(5x)/(2)`

Explanation:

Height of the person = 6 feet

Height of the lamppost = 10 feet

Let the distance between the man and end of shadow be = y

By using the concept of similar triangles:

`(y)/(6)=(x)/(10-6) }`

=>
`(y)/(6)=(x)/(4) }`

So, y =
`(3x)/(2)`

Now distance d will be = x + y

=
`x+(3x)/(2)`

d =
`(5x)/(2)`