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?
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
Thanks! So much!
To figure out the difference between the two poles, we can use similar triangles.
Let's assume the distance between the base of the first pole and the point where both shadows meet is "x" meters. Since the shadows overlap perfectly, we can say that the height of the shadow of the first pole is also "x" meters.
Using similar triangles, we can set up the following proportion:
(Shadow of the first pole) / (Height of the first pole) = (Shadow of the second pole) / (Height of the second pole)
x / 11 = (x + 13) / 8
To solve this equation, we can cross-multiply:
8x = 11(x + 13)
8x = 11x + 143
Subtract 11x from both sides:
8x - 11x = 143
-3x = 143
Divide both sides by -3:
x = -143 / -3
x = 47.67
So, the distance between the base of the first pole and the point where both shadows meet is approximately 47.67 meters.
To find the height difference between the two poles, subtract the height of the second pole from the height of the first pole:
11 - 8 = 3
Therefore, the difference between the two poles is 3 meters.