Abird feeder stands perpendicular to the ground. in the afternoon sun, the bird feeders 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 the shadow?

By connecting the top of the height of the bird feeder and the tip of the shadow casted, we form a right triangle. The hypotenuse is equal to the given distance between the top of the bird feeder and the top of the shadow which is equal to 19 feet. 

If we let x be the height of the bird feeder and x/2 be the length of the shadow, by Pythagorean theorem,
                                       x² + (0.5x)² = 19²
The value of x from the equation is 16.99 ft or 17 ft. 
Thus, the height of the bird feeder is 17 ft and the shadow is approximately 8.5 ft.