Top of a tree broke and fel over. Remaining tree trunk is 5 feet tall . Tip if tree rest on ground is 12 feet from the base of the trunk. What is the length of the broken tree?
17
No
Well, it seems the tree couldn't handle the pressure and decided to do the limbo! Now, let's get to the math-juggling part. If the remaining tree trunk is 5 feet tall and the tip of the fallen tree is 12 feet from the base of the trunk, we can use a bit of Pythagorean magic!
The length of the broken tree can be found by using the good old Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side (hypotenuse). In this case, the remaining tree trunk is the shorter side, and the length of the broken tree is the hypotenuse.
So, if we consider the remaining tree trunk as one side and the distance from the tip of the tree to the base as the other side, we get:
(5 feet)^2 + (12 feet)^2 = length of the broken tree^2
Simplify it a bit:
25 + 144 = length of the broken tree^2
169 = length of the broken tree^2
Taking the square root of both sides, we find that the length of the broken tree is:
√(169) = 13 feet
So, the length of the broken tree is 13 feet. I hope this answer leaves you pining for more!
To find the length of the broken tree, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the remaining tree trunk forms one side of the right triangle, and the length of the broken tree forms the hypotenuse.
Let's label the length of the broken tree as 'x'.
According to the given information, the height of the remaining tree trunk is 5 feet, and the distance from the base of the trunk to the tip of the fallen tree is 12 feet.
So, in this case, the vertical side of the right triangle is 5 feet, and the hypotenuse (the broken tree) is x feet.
We can use the Pythagorean theorem to set up the equation:
(Length of the broken tree)^2 = (Height of the remaining trunk)^2 + (Distance from the base to the tip)^2
x^2 = 5^2 + 12^2
Simplifying, we get:
x^2 = 25 + 144
x^2 = 169
To solve for x, we take the square root of both sides:
x = √169
x = 13
Therefore, the length of the broken tree is 13 feet.