2016 AMC 12B Problem 13

Alice and Bob live 10 miles apart. One day Alice looks due north from her house and sees an airplane. At the same time Bob looks due west from his house and sees the same airplane. The angle of elevation of the airplane is 30^\circ from Alice's position and 60^\circ from Bob's position. Which of the following is closest to the airplane's altitude, in miles?

\textbf{(A)}\ 3.5 \qquad\textbf{(B)}\ 4 \qquad\textbf{(C)}\ 4.5 \qquad\textbf{(D)}\ 5 \qquad\textbf{(E)}\ 5.5

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.