Question

From a ballon vertically above a straight road, the angles of depression of two cars at an instant are found to be 45' and 60'.If the cars are 100m apart find the height of the ballon(use root 3 = 1.73)

Answer 1

Solution:-
Let the two angle be x = 45° and y = 60° respectively.
And the distance between the two cars is d = 100 m
Height of balloon is AB  = h meter (See the figure)
Let BC = x meter
In triangle ABO,
tan 45° = AB/BO  ⇒ 1 = h/(x+100) ⇒ h = x + 100 ........(1)
In triangle ABC,
tan 60° = AB/BC 
⇒ √3 = h/x
⇒ h = x√3 ...... (2)
As h = x + 100
⇒ x + 100 = x√3
⇒ 100 = √3 x - x
⇒ 100 = x(√3 - 1)
⇒ x = 100/(√3 - 1)
⇒ x = 100 (√3 + 1)/(√3 - 1) (√3 + 1)/(√3 + 1)    {Multiplied by √3 +1 with both numerator and denominator}
⇒ x = 100(1.73 + 1)/2 
⇒ x = 100(2.73/2)
⇒ x = 273/2
⇒ x = 136.5 m
So, BC = 136.5 meter
So, h = x + 100
h = 136.5 + 100
h = 236.5 meter
Answer.

Answer 2

hope it will help you