Question Anand is 1.75 meters tall. At \( 10 \mathrm{a} . \mathrm{m} \)., he measures the length of a tree's shadow to be 41.35 meters. He stands 36.9 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
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To find the height of the tree, we can use similar triangles. Anand's height and the height of the tree, along with their respective shadows, form two similar triangles. The ratio of the heights to their shadow lengths will be equal. Let \( h \) be the height of the tree. We can set up the proportion as follows: \[ \frac{\text{Height of Anand}}{\text{Length of Anand's Shadow}} = \frac{\text{Height of Tree}}{\text{Length of Tree's Shadow}} \] Plugging in the values we know: \[ \frac{1.75 \, \text{m}}{41.35 \, \text{m}} = \frac{h}{36.9 \, \text{m}} \] Cross-multiplying gives us: \[ 1.75 \times 36.9 = h \times 41.35 \] Calculating \( 1.75 \times 36.9 \): \[ 64.275 = h \times 41.35 \] Now, to solve for \( h \): \[ h = \frac{64.275}{41.35} \] Calculating this gives: \[ h \approx 1.55 \, \text{m} \] Thus, the height of the tree, to the nearest hundredth of a meter, is approximately \( 1.55 \) meters.