A 5.5 foot tall woman is standing 14 feet from a streetlamp casts a six foot shadow. How high is the lamp?

The height of the lamp is  18.33 ft

Step-by-step explanation:

We can think in two triangle rectangles, one with cathetus of:

5.5ft and 6ft (the one formed by the woman ad her shadow)

And another triangle with cathetus equal to:

6ft + 14ft (the distance between the end of the shadow and the lamp)

And the other cathetus is the height of the lamp, H.

As bot triangles will share an angle (the one formed by the end of the shadow and the hypotenuse) then the triangles are equivalent, so the quotient between their cathetus will be equal, this is:

H/(6ft + 14ft) = 5.5ft/6ft

H/(20ft) = 5.5ft/6ft.

H = (5.5ft/6ft)*20ft = 18.33 ft

true? is that what you're asking or do you mean something else?