Question

On the side of a parade ground there are two flag poles. The first is 11m high and the second is 8m high. At 3pm the shadows cast by both poles overlap each other perfectly and the furthest point of both shadows is exactly 13m from the base of the base of the shortest pole. What is the difference between the the poles? Can you please explain how I figure this out?

Answer 1

draw a figure of a large triangle, end vertical height=11m
then draw a vertical 8 meters high somewhre in the triangle.

let the base of the small triangle be x, and y be the distance between the two vertical poles.

The triangles are similar:
x/8 = (x+y)/11

and, you re given x=13

13/8 =(13+y)/11
solve for y, the distance between the poles.

13*11/8 -13=y

y= 13(11/8-8/8)=13*3/8 meters

Answer 2

Thanks! So much!