An airplane flying at a height of 300 m notices the angles of depression to two boats located on opposite sides as 45° and 30°. Find the distance between the two boats.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. m.
Let the airplane be at point A, 300 m above the ground (point D)
Two boats are on opposite sides of point D.
Boat B with an angle of depression = 45°
Boat C with an angle of depression = 30°
Angles of depression = Angles of elevation from the boats
So, ∠ABD = 45° and ∠ACD = 30°
Height AD = 300 m
For Boat B: tan 45° = AD/DB
⇒ 1 = 300/DB
⇒ DB = 300 m
For Boat C: tan 30° = AD/DC
⇒ 1/√3 = 300/DC
⇒ DC = 300√3 m
Since boats are on opposite sides, the total distance BC = DC + DB
= 300√3 + 300
= 300(√3 + 1) m