To find the elevation of the aircraft, we first find the distance from one station to the aircraft, such as the side [latex]a[/latex], and then use right triangle relationships to find the height of the aircraft, [latex]h[/latex].

Because the angles in the triangle add up to 180 degrees, the unknown angle must be 180°−15°−35°=130°. This angle is opposite the side of length 20, allowing us to set up a Law of Sines relationship.

[latex]\begin{gathered} \frac{\sin \left(130^\circ \right)}{20}=\frac{\sin \left(35^\circ \right)}{a} \\ a\sin \left(130^\circ \right)=20\sin \left(35^\circ \right) \\ a=\frac{20\sin \left(35^\circ \right)}{\sin \left(130^\circ \right)} \\ a\approx 14.98 \end{gathered}[/latex]

The distance from one station to the aircraft is about 14.98 miles.

Now that we know [latex]a[/latex], we can use right triangle relationships to solve for [latex]h[/latex].

[latex]\begin{gathered}\sin \left(15^\circ \right)=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin \left(15^\circ \right)=\frac{h}{a} \\ \sin \left(15^\circ \right)=\frac{h}{14.98} \\ h=14.98\sin \left(15^\circ \right) \\ h\approx 3.88 \end{gathered}[/latex]

The aircraft is at an altitude of approximately 3.9 miles.