At a certain time of day, a tree that is x meters tall casts a shadow that is x−21 meters long. If the distance from the top of the tree to the end of the shadow is x+3 meters, what is the height, x, of the tree?
\(x^2 + (x-21)^2 = (x+3)^2\)
\(x^2 + x^2 + 441 - 42x = x^2 + 9 + 6x\)
\(x^2 - 48x + 432 = 0\)
Use quadratic formula: \(x = {48 \pm \sqrt{(-48)^2-4*1*432} \over 2}\)
\(48 \pm 24 \over 2 \)
x = 12, 36
But, shadows can't be negative so the answer is 36.
