At a certain time of day, a tree that is x meters tall casts a shadow that is x−49 meters long. If the distance from the top of the tree to the end of the shadow is x+1 meters, what is the height, x, of the tree?

60 meters

Step-by-step explanation:

(x+1)² = x² + (x-49)²

x²+2x+1 = x² + x²-98x+2401

x² - 100x + 2400 = 0

x² - 60x - 40x + 2400 = 0

x(x - 60) - 40(x - 60) = 0

(x - 40)(x - 60) = 0

x = 40, 60

If x = 40, x - 49 = -9 which is not possible

So x = 60m