Question

Straight highway leads to the foot of a tower a man standing at the top of the tower observes a car at an angle of depression of 30 degree which is approaching the foot of the tower with a uniform speed after covering a distance of 50m the angle of depression of the car becomes 60 find the height of the tower use root 3 is equal to 1.73

Answer 1

Height of the tower is 43.3m

•In triangle ABC

•tan 60° = P/B = AB/BC =h/d

• √3 = h/d

• d = h/√3 ______(1)

•In triangle ABD

•tan 30° = P/B = AB/BD =h/(d +50)

• 1/√3 = h/(d+50)

• d+50 = √3h

•h/√3 + 50 = √3h

•50 = h(√3-1/√3)

•50 = h (3-1)/√3

•50 = 2h/√3

•h = 25√3

•h = 25×1.732

•h = 43.3 m

Answer 2

Height of Tower =  43.25 m

Step-by-step explanation:

Height of tower = H m

Height of Man ignored

Let say distance  of Car initially from tower horizontally = d m

Tan 30° = h/d

=> 1/√3 = h/d

=> d = h√3

after covering a distance of 50m

=> distance  of Car from tower horizontally = d - 50 m

= h√3 - 50 m

angle of depression of the car becomes 60°

=> Tan60°  =  h/(h√3 - 50)

=> √3 =  h/(h√3 - 50)

=> 3h -  50√3 = h

=> 2h = 50√3

=> h = 25√3

√3 = 1.73

=> h = 25 * 1.73

=> h = 43.25 m

Height of Tower =  43.25 m

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