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Find the side length and the area

Source: Vietnam NMO 1963 Problem 5

February 2, 2009
geometrytrigonometrygeometry unsolved

Problem Statement

The triangle ABC ABC has semiperimeter p p. Find the side length BC BC and the area S S in terms of ∠A \angle A, ∠B \angle B and p p. In particular, find S S if p≈23.6 p \approx 23.6, ∠A≈52∘42′ \angle A \approx 52^{\circ}42', ∠B≈46∘16′ \angle B \approx 46^{\circ}16'.
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