An airplane is at an altitude of 1200 m, the angle of depression to a building at the airport on the ground measures 28∘. Find the distance from the plane to the building. Round your answer to the nearest tenth. Hint: Find the hypotenuse. The distance from the plane to the building is meters.

The distance from the plane to the building is ___2553.2___meters.

Step-by-step explanation:

Given that An airplane is at an altitude of 1200 m.

The angle of depression to a building at the airport on the ground measures 28°.

We need to find the distance from the plane to the building.

Please check the attached diagram.

Let 'x' be the required distance in meters.

It forms a right-angled triangle as shown in the attached diagram.

The angle = Ф =  28°

The opposite to angle = 1200 meters

All we need to find the hypotenuse to determine the distance from the plane to the building.

Using the trigonometric ratio

sin θ = Perpendicular ÷ Hypotenuse

sin (28°) = 1200 ÷ x

x = 1200/sin (28°)

  = 1200 / 0.47         ∵ sin (28°) = 0.47

   = 2553.2 m

Thus, the distance from the plane to the building is ___2553.2___meters.