A tree is struck by lightning. The top part breaks and falls to the ground. The part of the tree still standing is 30 feet tall and the top part that hit the ground is 40 feet from the base of the tree. How tall was the tree originally?
Assuming that the 40 is the length that fell and not its distance from the tree,
30 +40 = ?
30 squared + 40 squared = x squared
900 + 1600 = x squared
2500 = x squared
Therefore, x = root 2500
X= 50 feet
To determine the original height of the tree, we can use the concept of similar triangles.
First, let's label the given information:
- Height of the remaining part of the tree (standing part): 30 feet
- Distance from the base of the tree to where the top part hits the ground: 40 feet
Now, we can set up a proportion between the similar triangles formed by the remaining part of the tree and the fallen top part of the tree.
Let's assume that the original height of the tree is represented by 'h'. Then, we can set up the following proportion:
(h - 30) / 30 = h / 40
Now, we can cross-multiply and solve for 'h':
40(h - 30) = 30h
40h - 1200 = 30h
Subtract 30h from both sides:
40h - 30h - 1200 = 0
10h - 1200 = 0
Add 1200 to both sides:
10h = 1200
Divide both sides by 10:
h = 120
Therefore, the original height of the tree was 120 feet.