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At a certain distance, the angle of elevation to the top of a building is 60°. From 40 feet further back, the angle of elevation is 45°. Find the height of the building.

 Feb 23, 2020
 #1
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Let  H  be the height of the bldg  and D  be  the original distance from the  buildng

 

So

 

tan 60  =    H  / D 

cot 60 =  D /H

H cot 60  =  D

 

 

And we have that

 

tan   45  =   H  / ( D + 40)

  1  =  H / ( D + 40)

D + 40  =  H

H cot 60 + 40  = H

40  = H ( 1 - cot 60)   

40 / (1 - cot 60) = H  ≈  94.64  ft

 

 

cool cool cool

 Feb 23, 2020

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