{"status": "success", "data": {"description_md": "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?\n\n$\\textbf{(A)}\\ 3.5 \\qquad\\textbf{(B)}\\ 4 \\qquad\\textbf{(C)}\\ 4.5 \\qquad\\textbf{(D)}\\ 5 \\qquad\\textbf{(E)}\\ 5.5$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Alice and Bob live  <span class=\"katex--inline\">10</span>  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  <span class=\"katex--inline\">30^\\circ</span>  from Alice&#8217;s position and  <span class=\"katex--inline\">60^\\circ</span>  from Bob&#8217;s position. Which of the following is closest to the airplane&#8217;s altitude, in miles?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 3.5 \\qquad\\textbf{(B)}\\ 4 \\qquad\\textbf{(C)}\\ 4.5 \\qquad\\textbf{(D)}\\ 5 \\qquad\\textbf{(E)}\\ 5.5</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2016 AMC 12B Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12B_p14", "prev": "/problem/16_amc12B_p12"}}