Question

a balloon moving with the wind at a height of 1500 m horizontally above the ground is observed at a certain point on earth to subtend an angle of 60 . after sometime the angle of elevation reduces to 30 . find the distance travelled by the baloon during the interval .

Answer 1

this is the easiest questions you can do itb

Answer 2

E and D are balloon points. B and C are ground level. A be the observation point

Now in ΔABE,

tan 60° =  EB /AB

⇒ AB =  EB / tan 60 ⁰

         =   1500 √ 3

         = 500 √ 3

Now in ΔADC,

tan 30° =  DC/AC

⇒ AC =  DC /tan 30 ⁰  

          = 1500 ( 1 √ 3 )

          = 1500 √ 3

Now BC = AC - AB = 1500√3 - 500√3 = 1000√3 m = 1000 × 1.732 = 1732 m

Hence distance travelled by balloon during that interval = 1732 m.