Question

The angle of depression of two ships from an aeroplane flying at height of 7500m are 30 degree and 45 degree if both the ships are in same line that one ship is behind other find the side such distance between the ships

Answer 1

Answer:

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Answer 2

Given:

The angle of depression of ship A = 30°

The angle of depression of ship B = 45°

Height of flying airplane = 7500 meters

To Find:

The distance between the two ships.

Solution:

Assume that 'x' is the distance between ships A and B.

We can form two triangles if joining the airplane and ship's locations.

In triangle 1 with the angle of depression of 30°,

tan A = height of airplane/ distance from foot of airplane to the ship A

⇒ tan A = 7500/ x+y

⇒ tan A = tan 30° = 1/√3

On equating both,

⇒ x + y = 7500√3

In triangle 2 with angle of depression = 45°

tan B = height of airplane / distance between the ships

⇒ tan B = 7500/ y

⇒ tan B = tan 45° = 1

On equating both,

⇒ y = 7500 meters

Replacing the value of 'y'

⇒ x + y = 7500√3

⇒ x = 7500√3 - y ⇒ 7500√3 - 7500

⇒ x = 7500 (√3 - 1) meters

⇒ x = 5490 meters

Hence, the distance between ships A and B is 5490 meters.