Question

The angle of depression from the top of a building to a point

Answer 1

The distance between point on the ground from the top of the building is 396 meter, if the building is 280 m high and The angle of depression from the top of a building to a point  on the ground is 45 degrees.

Step-by-step explanation:

The given is,

                 The angle of depression from the top of a building to a point  on the ground is 45 degrees.

                 Height of the building is 280 meter.

Step: 1

                 Given diagram is a right angled diagram,

                 For right angle triangle,

                              90° = 45° + 45°    

                                     = 90°  

                 Trignometric ratio,

                            sin ∅ = $\frac{Opp}{Hyp}$....................(1)

                For the above ratio take the bottom angle, that is angle of depression from the top of a building to a point  on the ground is 45 degrees.

                 Where, Opp side = 280 meters

                               Hyp side = x

                                           ∅ = 45°

                 Equation (1) becomes,

                                  sin 45° = $\frac{280}{x}$

                          0.70710678 =  $\frac{280}{x}$

                                            x =  $\frac{280}{0.70710678}$

                                            x = 395.979

               Distance between point on the ground from the top of the building,  x ≅ 396 meter                                                

                Trignometric ratio,

                                     cos ∅ = $\frac{Adj}{Hyp}$

                                   Cos 45 = $\frac{Adj}{396}$

                                         Adj = (0.70710678)(396)

              Bottom length, Adj = 280 meter

Result:

           The distance between point on the ground from the top of the building is 396 meter.