To solve this problem, we can visualize a right triangle formed by the tree, its shadow, and the line connecting the top of the tree to the end of the shadow.
-
Heights and Shadows:
- The height of the tree (vertical leg of the triangle) is 24 feet.
- The length of the shadow (horizontal leg of the triangle) is 10 feet.
-
Forming a Right Triangle: The right triangle has:
- One leg (tree height) = 24 feet
- Another leg (shadow length) = 10 feet
-
Using the Pythagorean Theorem: According to the Pythagorean theorem, the relationship in a right triangle is given by: \[ c^2 = a^2 + b^2 \] where \( c \) is the hypotenuse (the distance from the top of the tree to the end of the shadow), and \( a \) and \( b \) are the other two legs.
In this case:
- \( a = 24 \) feet (tree height)
- \( b = 10 \) feet (shadow length)
Plugging in the values: \[ c^2 = 24^2 + 10^2 \] \[ c^2 = 576 + 100 \] \[ c^2 = 676 \] Taking the square root to find \( c \): \[ c = \sqrt{676} = 26 \]
-
Final Result: The distance from the top of the tree to the top of its shadow is \( 26 \) feet.