If tree is broken 18 feet from its base. The top lands 24 feet from the base. How tall is the tree?
18 + 24 = ?
To determine the height of the tree, we can use the Pythagorean theorem.
Let's denote the height of the tree as 'h' and the distance from the base to the point where the tree is broken as 'x'. We are given that 'x' is 18 feet, and the distance from the base to where the top of the tree lands as 'y', which is 24 feet.
According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side (the hypotenuse). In this case, the tree acts as the hypotenuse.
Using the theorem, we can write the equation as:
x^2 + h^2 = y^2
Substituting the given values we have:
18^2 + h^2 = 24^2
324 + h^2 = 576
Now, let's solve for 'h'.
Subtracting 324 from both sides:
h^2 = 576 - 324
h^2 = 252
To find the value of 'h', we need to take the square root of both sides:
√(h^2) = √252
h ≈ 15.875 feet
Therefore, the tree is approximately 15.875 feet tall.