An 18 m tall tree is broken during a severe storm. The distance from the base of the trunk to the point where the tip touches the ground is 12 m. At what height did the tree break?
the standard 5-12-13 triangle fits the bill, but algebraically,
If the tree broke at height x,
12^2 + x^2 = (18-x)^2
x = 5
x^2 + 12^2 = (18-x)^2
x^2 + 144 + x^2 - 36x + 324
144 = -36x + 324
-180 = -36x
-180/-36 = -36x/-36
5 = x
Mehtab made a slight error in his second step,it was suppose to be = instead or +
Well, that's what I call a "fallen comedy"! It seems like the tree just couldn't "leaf" well enough alone. Anyway, let's get to the bottom of this.
If the distance from the base to the point where the tip touches the ground is 12 m, and the tree is 18 m tall, then we can subtract the distance from the base to get the height of the broken part.
So, if we take 18 m (the total height) and subtract 12 m (the distance from the base), we get... *drumroll*... a broken height of 6 m! Looks like the tree just couldn't handle the "windustry" conditions.
To determine the height at which the tree broke, we need to find the vertical distance from the base of the trunk to the point where it broke.
Let's break down the problem step by step:
1. Start with the given information: The tree is 18 meters tall, and the distance from the base of the trunk to the point where the tip touches the ground is 12 meters.
2. Since we know the total height of the tree is 18 meters and the distance from the base to the ground is 12 meters, we can find the remaining height above the broken point by subtracting the distance from the base to the broken point from the overall height of the tree.
Remaining height = Total height - Distance from the base to the broken point
Remaining height = 18 m - 12 m
Remaining height = 6 meters
3. Therefore, the tree broke at a height of 6 meters from the base.
In summary, the tree broke at a height of 6 meters above the base of the trunk.