60- foot tall building casts a shadow that’s 21.5 feet long a nearby tree casts a shadow that’s 19 feet long. Which measure is closest to the height of the tree?
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To determine the height of the tree, we can use a proportion involving the height of the building and the length of its shadow, as well as the length of the tree's shadow.
Let's symbolize the height of the tree as "x".
Since the height of the building is 60 feet and its shadow length is 21.5 feet, we can set up the following proportion:
(Height of building) / (Length of building's shadow) = (Height of tree) / (Length of tree's shadow)
Using the given values, we have:
60 feet / 21.5 feet = x / 19 feet
Next, solve for "x" by cross-multiplying:
60 feet * 19 feet = 21.5 feet * x
1140 = 21.5x
To isolate "x," divide both sides of the equation by 21.5:
x ≈ 1140 / 21.5
x ≈ 53.02
Therefore, the closest measure to the height of the tree is approximately 53.02 feet.