George, who is 6.25-feet tall, needs to know the height of a tree that he is going to cut down. He notices that he casts a 10-foot shadow when the tree casts a 28-foot shadow. The height of the tree is feet tall. Enter only the number.
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Well, George is 6.25 feet tall and his shadow is 10 feet long. So, if we do some shadow math, we can find out the height of the tree! The ratio of George's height to his shadow length is 6.25 feet / 10 feet. Now, let's apply that same ratio to figure out the height of the tree. The tree's shadow is 28 feet long, which means the tree must be 6.25 feet / 10 feet * 28 feet tall. Crunching the numbers, we find that the tree is 17.5 feet tall. Ta-da! Now George knows exactly how tall that tree is.
To find the height of the tree, we can set up a proportion using the height and shadow lengths.
Let's call the height of the tree "h" feet.
The proportion can be written as:
6.25 feet / 10 feet = h feet / 28 feet
To solve for h, we can cross-multiply and solve the equation:
10 * h = 6.25 * 28
h = (6.25 * 28) / 10
h = 175 / 10
h = 17.5
Therefore, the height of the tree is 17.5 feet.
To find the height of the tree, we can use a method called similar triangles. Similar triangles have the same shape but can be different sizes. In this case, we have two triangles: one formed by George, his shadow, and his height, and another formed by the tree, its shadow, and its height.
Let's denote the height of the tree as 'x' (in feet). We can set up a proportion using the ratios of the corresponding sides of the two triangles:
(George's height) / (George's shadow) = (Tree's height) / (Tree's shadow)
Plugging in the given values, we get:
6.25 ft / 10 ft = x ft / 28 ft
To solve for x, we need to cross-multiply and then divide:
(6.25 ft) * (28 ft) = (10 ft) * (x ft)
175 ft = 10x ft
Dividing both sides by 10, we find:
175 ft / 10 = x ft
x = 17.5 ft
Therefore, the height of the tree is 17.5 feet.
George's height / shadow = 6.25 / 10 = 0.625
For a tree:
Tree's height / shadow is also 0.625
height / shadow = height / 28 = 0.625
height = 28 ∙ 0.625 = 17.5 ft
only the number = 17 ft