Answer to Question #315533 in Geometry for nickname826

Question

A bird feeder stands perpendicular to the ground. In the afternoon sun, the bird feeder's shadow is half its height. If the distance between the top of the bird feeder and the top of the shadow is 19 feet, how tall is the bird feeder and how long is its shadow?

please explain to me how you got the answer

Answer 1

Let feeder's height be x

Let Feeder's shadow be x/2

Distance from top of feeder to shadow = 19ft(hypotenuse)

Using Pythagoras' theorem

19² = x² + (x/2)²

361 = x² + (x²/4)

Multiply through by 4

1444 = 4x² + x²

1444 = 5x²

x = $\sqrt{1444/5}$ = 38/$\sqrt{5}$

Feeder's height = (38/$\sqrt{5}$ )

Feeder's shadow = (38/$\sqrt{5}$ )/2

= 19/$\sqrt{5}$