Question

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.(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we can use the Pythagorean theorem. Let x be the distance from the top of the tree to the top of its shadow.

We can set up the equation with the height of the tree (24 feet) as one leg of the right triangle, the distance from the top of the tree to the top of its shadow (x) as the other leg, and the length of the shadow (10 feet) as the hypotenuse:

24^2 + x^2 = 10^2
576 + x^2 = 100
x^2 = 100 - 576
x^2 = 476
x = sqrt(476)
x = sqrt(4 * 119)
x = 2 * sqrt(119)
x ≈ 2 * 10.91
x ≈ 21.82 feet

Therefore, the distance from the top of the tree to the top of its shadow is approximately 21.82 feet.

Now, to apply a Pythagorean triple, let's note that 24, 10, and 26 form a Pythagorean triple. So, in this case, the distance from the top of the tree to the top of its shadow can also be 26 feet.