Question

A pole projected outwards and upwards from a window at height of 8m above the ground level makes and angle of 30 degree with the wall if angle of elevation of base and tope of pole from the ground level is 30 degrees and 60 degrees, find the length of the pole

Answer 1

Let AB be the length of the window above which the pole of Height BC is Mounted
Let E be the base of the wall in front for which the height is ED

According to question, 
                                            AB = 8 m
Also angle of elevation from top of the pole to the top of the wall is

                          Angle CDB = 30 degree

Also, angle of elevation from the top of window to the base of wall
 
                        Angle BEA = 30 degree

Angle of elevation from the top of the pole to the base of wall

                       Angle CEA = 60 degree

Now in triangle BEA,
 
                            tan 30 degree = AB / AE
                                   1 / root 3 = 8 / AE
                                       AE  =  8 root 3
Now in triangle ACE
, 
                             tan 60 degree = AC / AE
                                   root 3 = (AB + BC) / AE
                                   root 3 = (8 + BC) / 8 root 3
                                   8 * 3 = 8 + BC
                                       BC = 24 - 8 = 16 m
Thus height of the pole is 16 m