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A pine tree casts a shadow that is 12 meters long. A maypole near the pine tree casts a shadow that is 6 meters long. If the pine tree is 16 meters tall, how tall is the maypole? Write your answer as a whole number or a decimal. Do not round

User Sai Tej
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1 Answer

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Final answer:

By setting up a proportion based on the similar triangles formed by the shadows and heights of the pine tree and maypole, and solving it, we find that the maypole is 8 meters tall.

Step-by-step explanation:

To find the height of the maypole, we can use the similar triangles formed by the shadows and the actual heights of the pine tree and the maypole. The ratios of the corresponding sides of similar triangles are equal. This means that the ratio of the pine tree's height to its shadow's length is equal to the ratio of the maypole's height to its shadow's length.

The pine tree and its shadow form one triangle with a height of 16 meters and a shadow length of 12 meters. The maypole and its shadow form the other triangle, with an unknown height and a shadow length of 6 meters. Setting up a proportion, we have:

Height of Pine Tree / Shadow of Pine Tree = Height of Maypole / Shadow of Maypole

16 meters / 12 meters = Height of Maypole / 6 meters

By cross-multiplying and solving for the height of the maypole:

16 meters * 6 meters = Height of Maypole * 12 meters

96 meters = Height of Maypole * 12 meters

Height of Maypole = 96 meters / 12 meters

Height of Maypole = 8 meters

Therefore, the maypole is 8 meters tall.

User Serge Belov
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