A 24-foot-tall tree casts a shadow that is 10 feet long. What is the distance from the top of the tree to the top of its shadow? Apply a Pythagorean triple to solve this problem.
The Pythagorean triple we can use for this problem is the 6-8-10 triangle, where the two legs are 6 and 8 units long, and the hypotenuse is 10 units long.
In this case, the height of the tree (the vertical leg of the right triangle) is 24 feet, and the length of the shadow (the horizontal leg of the right triangle) is 10 feet.
So, using the Pythagorean theorem:
(Height of tree)^2 + (Length of shadow)^2 = (Distance from top of tree to top of shadow)^2
(24)^2 + (10)^2 = (Distance)^2
576 + 100 = (Distance)^2
676 = (Distance)^2
Taking the square root of both sides:
Distance = √676
Distance = 26 feet
Therefore, the distance from the top of the tree to the top of its shadow is 26 feet.