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A 40 ft. tall tree casts a shadow that is 52 ft. long. A nearby building casts a shadow that is 166 ft. long. How tall is the building?

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Answer:

[tex]Suppose:\\AB = Height ~of ~the ~Building=?\\CD = Height ~of ~the ~tree = 40ft.\\CE = Length~of~shadow~of~tree = 52ft.\\BE = length~of~shadow~of~building = 166ft\\In~right~angled~triangle~ADE,\\tanE = \frac{CD}{CE} \\or, tanE = \frac{40}{52}........(1)\\In~right~angled~triangle~ABE,\\tanE=\frac{AB}{BE} \\or, tanE = \frac{AB}{166} \\Using~ eq^{n} (1), \\\frac{40}{52} =\frac{AB}{166} \\or, AB = \frac{40}{52}(166)\\or, AB = 127.69ft.\\So, ~the~height~of~the~building~is~127.69ft.[/tex]

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