An airplane pilot over the Pacific sights an atoll at an angle of depression of 10 degrees. At this time, the horizontal distance from the airplane to the atoll is 5,172. What is the height of the plane to the nearest meter?

Solution:

The problem statement has been summarised in the diagram below:

Using the trigonometric identity below we can determine AB

(Please Note: Atoll is kind of a small piece of partially submerged land in the sea or ocean)

The horizontal distance between points B and C is 5172 meters. To ascertain the height at which the plane is the following trigonometric ratio will be used:

Tan θ = Perpendicular/Base = AB/BC

Where θ = 10°

tan 10° = h/5172

tan 10° = 0.1764

Therefore,

h = tan10° × 5172 metres = 912.34 metres

The plane is at a height of 912.34 meters when it sights the atoll 5172 meters away.

An airplane pilot over the Pacific sights an atoll at an angle of depression of 10 degrees. At this time, the horizontal distance from the airplane to the atoll is 5,172. What is the height of the plane to the nearest meter?

Summary:

An airplane pilot over the Pacific sights an atoll at an angle of depression of 10 degrees. At this time, the horizontal distance from the airplane to the atoll is 5,172. The height of the plane to the nearest meter is 912 metres.