Question

from her elevated observation post 300m away, a naturalist spots a troop of baboons high up in a tree. Using the small transit attached to her telescope, she finds the angle of depression to the bottom of this tree is 30°, while the angle of elevation to the top of the is 60°. The angle of elevation to the troop of baboons is 45°. Use this information to find the height of the observation post, the height of baboons tree and the height of the baboons above the ground.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

( a ) Height of the observation post = 100$\sqrt{3}$ meter.

( b ) Height of baboons tree = 400 $\sqrt{3}$ meter.

( c ) Height of baboons above the ground = 100 ($\sqrt{3}$ + 1) meter.

Given

To find the,

( a ) Height of the observation post

( b ) Height of baboons tree

( c ) Height of baboons above the ground.

From the figure,

                         CD = AB = h meters

                         FE = $h_1$ meter

                         DE = $h_2$ meter

                          AD = BC = 300 meter.

( a ) Finding height of the observation post :

                             tan 30° = h / 300

                                  $\frac{1}{\sqrt{3} }$ = h / 300

                                   h = 300 / $\sqrt{3}$

                                      = (100×3) / $\sqrt{3}$

                                    h = 100$\sqrt{3}$ meter.

( b ) Finding height of baboons tree :

               In ΔADF,        

                               tan 60° = $h_1$ / 300    

                                      $\sqrt{3}$ = $h_1$ / 300  

                                        $h_1$ = 300 $\sqrt{3}$                

      Height of baboons tree = h + $h_1$

                                              =  100$\sqrt{3}$ +  300 $\sqrt{3}$

                                              = 400 $\sqrt{3}$ meter.

( c ) Finding height of baboons above the ground :

              In ΔAED,

                              tan 45° =  $h_2$ / 300

                                      1 =  $h_2$ / 300

                                     $h_2$ = 300

       Height of baboons above the ground = h + $h_2$

                                                                       = 100$\sqrt{3}$ + 300      

                                                                       = 100 ($\sqrt{3}$ + 1) meter.

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