A man wants to remove a tall pine tree from his yard. Before he goes to home depot, he needs to know how tall an extension ladder he needs to purchase. He measure the shadow of the tree to be 225 feet long. At the same time he measures the shadow of a 4 foot stick to be 3 feet. Approximately how tall is the pine tree?
h/225 = 4/3
h = 300 ft
So, how long a ladder does it take to cut down a 300' tree?
Maybe he'd be better off to measure the diameter of the tree, so he can get a saw of appropriate size.
To find out the approximate height of the pine tree, we can use the concept of similar triangles. The ratio of the length of the shadow to the height of the object is the same for both the tree and the stick.
Let's denote:
- Length of the tree's shadow: T
- Height of the tree: H
- Length of the stick's shadow: S
- Height of the stick: 4 feet
Given that the length of the tree's shadow (T) is 225 feet and the length of the stick's shadow (S) is 3 feet, we can set up the proportion:
T/S = H/4
Let's solve for H, the height of the tree:
H = (T/S) * 4
Substituting the given values:
H = (225/3) * 4
H = 150 * 4
H = 600 feet
Therefore, the approximate height of the pine tree is 600 feet.
To determine the approximate height of the pine tree, we can use the concept of similar triangles.
Let's call the height of the pine tree "x".
According to the height and shadow measurements, we can set up the following proportion:
(height of tree / length of tree's shadow) = (height of stick / length of stick's shadow)
(x / 225) = (4 / 3)
To solve for x, we can cross-multiply:
3x = 4 * 225
3x = 900
Dividing both sides by 3, we find:
x = 900 / 3
x = 300
Based on these calculations, the approximate height of the pine tree is 300 feet.