Processing math: 100%
 
+0  
 
0
22
4651
1
avatar

From the top of a building 60 feet high, the angle of elevation of the top of a pole is 14 degrees. At the bottom of the building the angle of elevation of the top of the pole is 28 degrees. Find the distance from the pole to the building.

 Aug 27, 2014

Best Answer 

 #1
avatar+33654 
+5

Let h be the height of the pole and d be the distance from the building.

 

tan(28) = h/d   ...(1)

tan(14) = (h-60)/d  ...(2)

 

Rewrite (2) as tan(14) = h/d - 60/d   ...(3)

 

Use (1) in (3):     tan(14) = tan(28) - 60/d  ...(4)

 

Rearrange (4) to get d = 60/(tan(28)-tan(14))

 

d=60(tan360(28)tan360(14))d=212.4785622452215097

 

or d ≈ 212.5 ft

 Aug 27, 2014
 #1
avatar+33654 
+5
Best Answer

Let h be the height of the pole and d be the distance from the building.

 

tan(28) = h/d   ...(1)

tan(14) = (h-60)/d  ...(2)

 

Rewrite (2) as tan(14) = h/d - 60/d   ...(3)

 

Use (1) in (3):     tan(14) = tan(28) - 60/d  ...(4)

 

Rearrange (4) to get d = 60/(tan(28)-tan(14))

 

d=60(tan360(28)tan360(14))d=212.4785622452215097

 

or d ≈ 212.5 ft

Alan Aug 27, 2014

0 Online Users