Word problem dealing w/ height of a building

[lewch45]

Can someone help me with this one?

The angle of elevation to the top of a radio antenna on the top of a building is 53.4 degrees. After moving 200 feet closer to the building, the angle of elevation is 64.3 degrees. Find the height of the building if the height of the antenna is 180 feet.

Any help would be appreciated.

 

[royhaas]

Draw a picture first and think about the tangents of the angles involved.

 

[Unco]

G'day.

  At a distance x from the building, the angle of elevation to the
    antenna, with height (incl the building's height) h, is 53.4deg:

 /|\ |\
  |  |   \
     |      \
     |         \
  h  |            \
     |               \
     |               /  \
  |  |              /53.4  \
 \|/ |______________|_________\
  
     <-         x            ->
 
  After moving 200m towards the building, the distance to the 
    building is now x-200. The angle of elevation from here to 
    the antenna is 64.3deg:

 /|\ |\
  |  | \
     |  \
     |   \       
  h  |    \      
     |     \     
     |    / \    
  |  |  /64.3\   
 \|/ |_|______\________________
      x - 200  <-    200     ->
     <-      ->            
     <-           x          ->

 From the first triangle:

                 opp    h 
    tan(53.4) =  --- = ---   [1]
                 adj    x

 From the second triangle:

                 opp     h
    tan(64.3) =  --- = -----      [2] 
                 adj   x-200
    

  Make h the subject of [1] and [2], equate and solve for x.

  Use [1] or [2] with your value for x to find h.

  Remember that h includes the length of the antenna.