Question

An observer (0) spots a plane flying a 35° angle to his horizontal line of the sight. If the plane is flying at an altitude of 17,000 ft, what is the distance (x) from the plane (P) to the observer (O)?

Answer 1

Explanation:

To solve for the distance from the plane to the observor, you will use the sine of a 35 degree angle - which is approximately .5736.

A right triangle formed by these measurements has a side opposite the 35 degree angle at a length of 17,000 feet. Form an equation - using the sine of the 35° angle equal to the 17000 feet side divided by x - the distance in question - which is the hypotenuse of this diagram.

sin 35° =
`(opposite)/(hypotenuse)`

.5736 =
`(17000)/(x)`

.5736x = 17000

Divide both sides by .5736

x = 17000/.5736

x = 29639 (rounded)

Option C

Answer 2

Refer to the diagram shown below.

By definition,
sin(35°) = 17000/x
Therefore
x = 17000/sin(35°) = 29,638.6 ft

Answer: 29,638.6 ft