A Triangle from Three Clues

★ 5/10plane geometry Law of Sines trigonometry Law of Cosines

Problem

In triangle $ABC$ , the sides opposite angles $A, B, C$ are $a, b, c$ respectively. Given that

2\sin C = c\sin B, \qquad a\cos B - c = 1,

and the area of triangle $ABC$ is $\dfrac{\sqrt{3}}{2}$ , find $a$ .

Answer

Solution

Difficulty	5/10
Topics	plane geometry, Law of Sines, trigonometry, Law of Cosines

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