Question

The angle of elevation of the top of a flagpole from a point A on a level ground is 13°.The angle of elevation of the top of the flagpole from another point B nearer the pole and 12m from A is 300. Find;

1.  
   1. The height of the flagpole 
   2. The distance from point B to the top of the flagpole. 
2. Given that tan ∝ = 0.75, without using tables or a calculator find Cos (180 − ∝)

Answer 1

1.  
   1. 
      
      tan 13° =   h  
                    12+x
      h=(12+x)0.2308
      h=2.7704 + 0.2308x
      tan 30° = ^h/_x
      h = 0.5773x
      ∴2.7704 + 0.2308x = 0.5773x
      0.3465x = 2.7704
      0.3465      0.3465
               x = 7.995
               x  = 8m
      ∴ h = 0.5773 × 8 
         h= 4.616m
   2. 
      
      Cos 30° = ⁸/_H
      H=     8     
           Cos 30°
             = −⁴/₅
      H=9.24m
2. tan ∝ = ¾ (1 quadrant)
   Cos ∝ = ⁴/₅
   Cos (180 − ∝) = − Cos ∝