Question

An observer (O) spots a plane flying at a 42° angle to his horizontal line of sight. If the plane is flying at an altitude of 15,000 ft., what is the distance (x) from the plane (P) to the observer (O)?

A right triangle is shown with angle O marked 42 degrees, hypotenuse marked x and the height marked 15000 feet.

Answer 1

Let O represent the location of the observer,
and P represent the location of the plane
and x represent the distance from O to P as shown in the diagram below:

Answer 2

Then, \(x\) can be found by applying the sine function to the right triangle above:
\(\sin(\theta) = \dfrac{\text{opposite side}}{\text{hypotenuse side}}\)

Answer 3

@kayhoney, are you familiar with the setup above?