Subject: General Aptitude · Chapter: Heights and Distances · Exam: · Marks: · Difficulty:
A man standing on the bank of a 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 the angle to be 30°. Find the breadth of the river.
Answer
Answer (as printed):
Explanation
Let AB be the tree and AC be the river. Let C and D be the two positions of the man. Then, ∠ ACB = 60°, ∠ ADB = 30° and CD = 36 m. B Let AB = h metres and AC = x metres. Then, AD = (36 + x) metres. h AB 1 h 1 = tan 30° = ⇒ = AD 3 36 + x 3 30° 60° D 36 m C x A 36 + x ⇒ h = 3 AB h = tan 60° = 3 ⇒ = 3 AC x ⇒ h = 3x 36 + x From (i) and (ii), we get : = 3 x ⇒ x = 18 m. 3 So, the breadth of the river = 18 m.
Explanation as extracted from the printed page; notation may be imperfect.