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 how high is the airplane? round to the nearest hundredth of a mile.

Answer 1

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
`a` in triangle ABC:

`(a)/(sin(14)) = (5)/(sin(16))`

`a= (5sin(14))/(sin(16))`

`a=4.39`

Next, we are going to use the trig function Sine in triangle BCD to find the height,
`h`, of the plane:

`sin(30)= (h)/(4.39)`

`h=4.39sin30`

`h=2.19`

We can conclude that the plane is 2.19 miles high.