Question

An airplane flying parallel to the ground is observed at two points, first at an angle of elevation of 80 in the western sky and 2 minutes later at an angle of elevation of 60 in the eastern sky. The airplane has covered a distance of 12 km in the two minutes. How high off the ground is the plane flying? Answer to nearest tenth of a km.

Answer 1

The air plane is flying 16.43 km from the ground.

Step-by-step explanation:

The image of the air plane is given in the image.

(sin A)/a = (sin B)/b = (sin C)/c

From the diagram, we get,

180° - 80° - 60° = 40°

(sin 40)/12 = (sin 60)/x₁

x₁ = (sin 60 × 12)/(sin 40)

∴ x₁ = 0.642 km

(sin 80)/x₂ = (sin 40)/12

x₂ = (sin 80 × sin 40)/12

∴ x₂ = 0.0527 km

Now,

(sin 90)/0.0527 = (sin 60)/x

1/0.0527 = (sin 60)/x

x = (sin 60)/0.0527

∴ x = 16.43 km