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A man standing on the roof of a building 56.0 feet high looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his building to be 34.6°, while the angle of depression from the roof of his building to the bottom of the building next door is 63.7°. How tall is the building next door? (Round your answer to the nearest tenth.)

 Feb 17, 2020
 #1
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Call the  height of the  neighboring building, H

And call the  distance  between the buildings  = D

 

So we have that

 

tan(34°)  = [ 56 - H ] / D

 

D =  [56 - H ]/ tan (34°)

 

And we also  have that

 

tan (63.7)  =  56/ D   

 

tan (63.7)  = 56 /[ (56 -H) / tan(34) ]

 

tan (63.7)  = 56 tan (34) / [ 56 - H ]

 

[ 56 - H ] tan (63.7)  = 56 tan (34)

 

56 tan (63.7)   - H tan (63.7)  = 56 tan (34)

 

H tan (63.7) = 56 ( tan (63.7) - tan (34) ]

 

H =  56 [ tan (63.7) - tan (34) ] /  tan (63.7)  ≈   37.3  ft

 

 

cool cool cool

 Feb 17, 2020

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