Question

The pilot of an aeroplane observes that the angle of depression of a kilometer stone on a straight road on a horizontal groud is 30 degree when he aeroplane is at a particular altitude ehen he is increase the altitude by 300m the angle of depression of the nex kilometer stone is 60 degree. Find the altitude of the aeroplane

Answer 1

Answer:

1016 m

Step-by-step explanation:

The pilot of an aeroplane observes that the angle of depression of a kilometer stone on a straight road on a horizontal groud is 30 degree when he aeroplane is at a particular altitude ehen he is increase the altitude by 300m the angle of depression of the nex kilometer stone is 60 degree. Find the altitude of the aeroplane

Let Say Altitude of Aeroplane was =  H  m

Angle of depression = 30°

Horizontal Distance of kilometer stone = D  m

Tan 30° = H/D

=> D = H/Tan30°

Altitude increased by 300 m

New Altitude = H + 300 m

Angle of depression = 60°

Horizontal Distance of Next kilometer stone = D + 1000 m   ( 1km = 1000 m)

Tan60° = (H+300)/(D + 1000)

=> DTan60° + 1000 Tan60°  = H + 300

=> (H/Tan30°)Tan60° - H = 300 - 1000Tan60°

Tan30° = 1/√3   Tan60° = √3    √3 = 1.732

=> 3H - H = 300 - 1732

=> 2H = -1432

=> H = -716  which is not possible so something wrong with Data

Now Assuming that next km stone is towards aeroplane

then  

Horizontal Distance of Next kilometer stone = D - 1000 m

Tan60° = (H+300)/(D - 1000)

=> DTan60° - 1000 Tan60°  = H + 300

=> (H/Tan30°)Tan60° - H = 300 + 1000Tan60°

Tan30° = 1/√3   Tan60° = √3    √3 = 1.732

=> 3H - H = 300 + 1732

=> 2H = 2032

=> H = 1016

Height of Aeroplane was 1016 m