To find the height of the tree using the proportionality of the heights and shadow lengths, we can set up a ratio based on the information given.
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Convert your height from feet and inches to just feet.
- You are 5 feet 3 inches tall.
- There are 12 inches in a foot, so: \[ 3 \text{ inches} = \frac{3}{12} = 0.25 \text{ feet} \]
- Therefore, your height in feet is: \[ 5 + 0.25 = 5.25 \text{ feet} \]
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According to the problem, your shadow is 4 feet long and the tree's shadow is 16 feet long. We can set up the following proportion: \[ \frac{\text{Height of you}}{\text{Shadow of you}} = \frac{\text{Height of the tree}}{\text{Shadow of the tree}} \] Plugging in the known values: \[ \frac{5.25}{4} = \frac{h}{16} \] Here, \(h\) represents the height of the tree.
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Cross-multiplying to solve for \(h\): \[ 5.25 \times 16 = 4 \times h \] Calculating \(5.25 \times 16\): \[ 5.25 \times 16 = 84 \] So we have: \[ 84 = 4h \] Dividing both sides by 4 gives: \[ h = \frac{84}{4} = 21 \text{ feet} \]
Thus, the height of the tree is 21 feet.
So the correct answer from your options is 21 ft.
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