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Rational Number Or Not?

Source: 1983 National High School Mathematics League, Exam One, Problem 3

February 21, 2020

Problem Statement

In triangle ABCABC, AB=ACAB=AC, ∣BC∣|BC| and d(A,BC)d(A,BC) are both integers. Then, sin⁡A\sin A and cos⁡A\cos A (A)\text{(A)} one is a rational number while the other is not (B)\text{(B)} both are rational numbers (C)\text{(C)} neither is rational number (D)\text{(D)} not sure
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