A man standing on the bank of river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 36 m from the bank, he finds that the angle is 30°. The breadth of the river is

Question

নিচের অপশন গুলা দেখুন

• 15 m
• 18 m
• 11 m
• 16 m

Answer 1

সঠিক উত্তর হচ্ছে: 18 m

ব্যাখ্যা:

Given:

Angle subtended by the tree on the opposite bank = 60° 

Angle subtended by the tree 36 m backward from the bank = 30° 

Calculation:

Let the height of the treee be = h 

Let the breadth of the river be = a 

In triangle BCD, CD/BC = tan 60° 

⇒ h/a = √3 

⇒ a = h/√3                       .........(1) 

In triangle ACD, CD/AC = tan 30° 

⇒ h/(36 + a) = 1/√3                 

⇒ √3h = 36 + a 

⇒ a = √3h - 36                   .........(2) 

By comparing (1) and (2), we get

⇒  h/√3 = √3h - 36 

⇒ h = 3h - 36√3 

⇒ 2h = 36√3

⇒ h = 18√3 m 

By putting the value of h = 18√3 m in equation (1)

⇒ a = 18√3/√3  

⇒ a = 18 m 

∴ The breadth of the river is 18 m.