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smc

geometry senior

Problem

Alice and Bob live 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 from Alice's position and from Bob's position. Which of the following is closest to the airplane's altitude, in miles?
(A)
(B)
(C)
(D)
(E)
Solution
We have two 30-60-90 triangles and that are perpendicular and share leg (the altitude of the plane ). The shared leg is the shortest leg of one triangle and the longest leg of the other. and are Bob and Alice respectively. Find and in terms of . Use Pythagorean Theorem on triangle to produce
Final answer
E