Question

An aeroplane is flying at a height of 1500m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite direction is 45o and 60o respectively. Find the width of the river.

Answer 1

Question :-

An aeroplane is flying at a height of 1500m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite direction is 45° and 60° respectively. Find the width of the river.

Solution :-

Let height of the aeroplane (RS) = 1500 m and AS = x m and SJ = y m.

⭐ In ΔRSJ

↪ RS/SJ = tan45°

↪ 1500/y = 1

↪ y = 1500 m

⭐ In ΔRSA

↪ RS/AS = tan60°

↪ 1500/x = √3

↪ x√3 = 1500

↪ x = 1500 × √3 / √3 × √3

↪ x = 1500√3/3

↪ x = 500√3

↪ x = 500 × 1.732

↪ x = 866 m

⭐ AJ = AS + SJ (A - S - J)

↪ AJ = x + y

↪ AJ = 866 + 1500

↪ AJ = 2366 m

Hence,

• The width of the river is 2366m.