Question

An airplane is flying at a height of 200m. Its angle of elevation to an observer on the ground is 230. Calculate the distance of the airplane from the observer.

Answer 1

Distance between the plane and the observer is 511.86 miles.

Explanation:

From the figure attached,

A plane is flying at point A which is at 200 m height and observer is at point C.

Angle of elevation (∠ACB) of the plane from the observer is 23°.

Let the distance between the observer and the plane is x meters.

By applying sine ratio for angle C,

sin(∠C) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

sin(23°) =
`(200)/(x)`

x =
`\frac{200}{\text{sin}(23)}`

x = 511.86 miles

Therefore, distance between the plane and the observer is 511.86 miles.