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The angle of elevation to the top of a building is 45 degrees. If you move 20 feet farther away, the angle of elevation to the top of the building becomes 30 degrees. What is the height of the building (in feet)?

 May 4, 2020
 #1
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Let d  be  the  original distance to the building

Let h be the height of the building

 

Since the original  angle  of elevation is 45°, then d  =  h

 

So  when we move 20 feet back  we have that

 

tan 30°   =   d   / [d + 20]      rearrange as

 

[ d + 20] tan30°  =  d

 

d tan 30 + 20 tan 30°  = d

 

  20 tan 30°  =  d - dtan30°

 

20tan30° =  d ( 1 - tan 30°)

 

[ 20tan30° ] / [ 1 - tan 30°]  =  d  ≈ 27.32 ft  =  h

 

 

cool cool cool           

 May 4, 2020

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