Question

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.

Answer 1

Option C (2556.1 meters).

Explanation:

This question can be solved using one of the three trigonometric ratios. The height of the airplane from the ground is 1200 meters and the angle of depression is 28°. It can be seen that the required distance is given by x meters. This forms a right angled triangle, as it can be seen in the diagram. The perpendicular is given by 1200 meters, the hypotenuse is unknown, and the angle of 28° is given, as shown in the attached diagram. Therefore, the formula to be used is:

sin θ = Perpendicular/Hypotenuse.

Plugging in the values give:

sin 28 = 1200/x.

x = 1200/sin 28.

x = 2556.06536183 meters.

Therefore, the airplane is 2556.1 meters (to the nearest tenths) far away from the building!!!