You go to another forest and measure the shadow of a tree as being 6 meters long. The shadow of your meter stick is 2 meters long. How tall is the tree?
Answer (3)
Well, 6/n=3/1, so n=2.
To find the height of the tree, we utilize the concept of similar triangles. By setting up a proportion between the tree and its shadow and the meter stick and its shadow, we determine that the tree is 3 meters tall.
We can determine the height of the tree by using the concept of similar triangles, which is a part of triangulation in measurement and survey. In this case, we have two similar triangles: the big triangle formed by the tree and its shadow, and the small triangle formed by the meter stick and its shadow. Because the triangles are similar, the ratio of the height of the tree to the height of the meter stick is equal to the ratio of the length of the tree's shadow to the length of the meter stick's shadow.
To calculate the height of the tree (let's denote it as H), you can set up the proportion
H / 1 meter = 6 meters / 2 meters.
Solving for H gives you H = (6 meters / 2 meters) times 1 meter = 3 meters.
Therefore, the height of the tree is 3 meters.
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The height of the tree, based on the shadow measurements, is 3 meters. This is found using the proportions between the lengths of the shadows and the heights of the objects. By setting up a simple ratio, we can solve for the unknown height of the tree.
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