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 A 6-inch tall flower casts a 4-inch shadow at 5:00pm. One month later, when the sun was at the same position in the sky as it was at 5:00pm one month earlier, the shadow cast was 5 1/3 inches long. How many inches taller was the flower when it cast the 5 1/3-inch shadow than it was when it cast the 4-inch shadow?

 May 6, 2020
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Shadow is adjacent leg of right triangle    Height is the other opposite leg

tan = opp/adj = 6/4

arctan 6/4 = 56.31 degrees

 

Same angle a month later

tan (56.31) = opp/adj = height/(5 1/3)

height = 8 inches

 

 

or

a ratio    6/4 = x/(5 1/3)

 x =8

 

So the plant is 2 inches taller.

 May 6, 2020

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