When a tree 6.2 meters long casts a shadow 6.5 meters long, how long is a shadow cast by someone 2.2 meters tall?
since 2.2m is .35* 6.2, the shadow is .35*6.5 = 2.28
To find the length of the shadow cast by someone 2.2 meters tall, we can use the concept of proportions.
We know that the tree's height (6.2 meters) is proportional to the length of its shadow (6.5 meters). Let's assign variables to these values.
Let H be the height of the tree (6.2 meters).
Let S be the length of the tree's shadow (6.5 meters).
Let h be the height of the person (2.2 meters).
Let s be the length of the person's shadow (unknown).
Using the concept of proportionality, we can write the following equation:
(H/S) = (h/s)
Substituting the known values:
(6.2/6.5) = (2.2/s)
Now, we can solve for s by cross-multiplying:
6.2s = 6.5 * 2.2
6.2s = 14.3
Dividing both sides by 6.2:
s = 14.3 / 6.2
s ≈ 2.31 meters
Therefore, the shadow cast by someone 2.2 meters tall would be approximately 2.31 meters long.
To solve this problem, we can use the concept of similar triangles. Similar triangles have corresponding angles that are equal and corresponding sides that are proportional.
First, let's set up a proportion between the height of the tree and the length of its shadow:
Tree height / Tree shadow = Person height / Person shadow
Let's assign variables to the given information:
Tree height = 6.2 meters
Tree shadow = 6.5 meters
Person height = 2.2 meters (which we have to find)
Person shadow = ?
Now we can substitute these values into the proportion:
6.2 / 6.5 = 2.2 / Person shadow
To find the length of the person's shadow, we need to isolate the "Person shadow" term. We can do this by cross-multiplying:
6.2 * Person shadow = 6.5 * 2.2
Now, let's solve for Person shadow:
Person shadow = (6.5 * 2.2) / 6.2
Calculating this expression will give us the length of the person's shadow.
Person shadow = 2.3 meters (rounded to one decimal place)
Therefore, the length of the shadow cast by someone who is 2.2 meters tall will be approximately 2.3 meters based on the given proportions.