An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. they report the angles of elevation as 14° and how high is the airplane? round to the nearest hundredth of a mile.

The complete question: 
An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. they report the angles of elevation as 14° and 30° how high is the airplane? round to the nearest hundredth of a mile.

Check the diagram of the situation in the picture attached.

First, we are going to use the law of sines to find the measure of side [tex]a[/tex] in triangle ABC:
[tex] \frac{a}{sin(14)} = \frac{5}{sin(16)} [/tex]
[tex]a= \frac{5sin(14)}{sin(16)} [/tex]
[tex]a=4.39[/tex]

Next, we are going to use the trig function Sine in triangle BCD to find the height, [tex]h[/tex], of the plane:
[tex]sin(30)= \frac{h}{4.39} [/tex]
[tex]h=4.39sin30[/tex]
[tex]h=2.19[/tex]

We can conclude that the plane is 2.19 miles high.