A monument casts a 40 -foot shadow. Adam is 6 feet tall and casts a 5 -foot shadow. How tall is the monument? A. 48 ft B. 33 ft C. 40 ft D. 30 ft
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To find the height of the monument, we can use the principle of similar triangles. Since the lengths of shadows and heights are proportional, we can set up a proportion: \(\frac{\text{Height of the monument}}{\text{Shadow of the monument}} = \frac{\text{Height of Adam}}{\text{Shadow of Adam}}\) Substituting in the values: \(\frac{h}{40} = \frac{6}{5}\) Cross multiply to solve for \(h\): \(5h = 240\) Therefore, \(h = 48\) feet. The correct answer is A. To visualize this, think of how shadows stretch on a sunny day. Just like how a tall tree will cast a longer shadow than a small flower, proportions remain intact in similar triangles around us!
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