Question

An airplane, flying at an altitude of 6 miles, is on a flight path that goes directly over you. If θ is the angle of elevation, find the distance from the observer to the plane. Note, the picture below is not to scale. Find the distance from the person to the plane if θ = 30° (without a calculator, show all work).

Answer 1

Answer:

Distance between the person and the plane is 12 miles

Step-by-step explanation:

From the figure attached,

An airplane is flying at an altitude AB = 6 miles.

An observer is standing at point C from where he observes the plane at an angle of elevation θ

Therefore, sinθ = $\frac{\text{\text{Opposite side}}}{\text{Hypotenuse}}$

sinθ = $\frac{AB}{AC}$

AC = $\frac{AB}{sin\theta }$

AC = 6cosecθ

If angle θ = 30°

Then AC = 6cosec30

AC = 6×2

AC = 12 miles

Therefore, distance between the person and the plane is 12 miles.