Question

(4)A boy standing in the middle of a field,
observes a flying bird in the north at an angle
of elevation of 30° and after 2 minutes, he
observes the same bird in the south at an
angle of elevation of 60°. If the bird flies all
along in a straight line at a height of then its
speed in km/h is:​

Answer 1

Speed of the bird is 6 km/h.

Given

To find the speed of the bird in km/h.      

Bird flying in the North at an angle of elevation = 30°

After 2 minutes,

Bird flying in the South at an angle of elevation = 60°

Bird flies in a straight line at a height = 50$\sqrt{3}$ m.

From the figure,

                         AB = CD = height = 50$\sqrt{3}$ m

In ΔOAB,      

              tan 30° = $\frac{AB}{OA}$

                     $\frac{1}{\sqrt{3} }$ = $\frac{50\sqrt{3} }{OA}$

                     OA = 50$\sqrt{3}$ × $\sqrt{3}$

                            = 50 × 3 = 150

                      OA = 150 m.

In ΔOCD,

               tan 60° = $\frac{CD}{OC}$

                       $\sqrt{3}$ = $\frac{50\sqrt{3} }{OC}$

                        OC = 50

                        OC = 50 m.

The total distance, AC = OA + OC

                                     = 150 + 50

                                     = 200

                               AC = 200 m.

Where, AC = BD = 200 m.                      

Speed of the bird = 200/2 = 100

                              = 100 m/min.

To convert m/min to km/hr

        Speed of the bird = $\frac{100}{1000}$ × 60

                                      = 6 km/h.

Therefore, speed of the bird is 6 km/h.

To learn more...

1. brainly.in/question/278594

2. brainly.in/question/787688