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# Law of Sines: Difficult Problems with Solutions

Problem 1
In triangle ABC, $$BC=\sqrt{3}$$, AC=2. If $$\angle ABC=60^{\circ}$$, find $$\sin \angle BAC$$.
In the answer box, write the fraction in the form a/b.
Problem 2
In the acute triangle ABC, $$BC=2\sqrt{3}$$, AC=2. If $$\angle ABC=30^{\circ}$$, find $$\angle BAC$$ in degrees.
Problem 3
In triangle ABC, $$BC=5$$, AC=3. If $$\sin\angle ABC=\frac{2}{5}$$, find $$\sin \angle BAC$$.
In the answer box, write the fraction in the form a/b.
Problem 4
In triangle ABC, $$BC=5$$, $$AC=7\sqrt{2}$$. If $$\angle ABC=45^{\circ}$$, find $$\sin \angle BAC$$.
In the answer box, write the fraction in the form a/b.
Problem 5
In triangle ABC, $$BC=5$$, AC=9. If $$\sin\angle ABC=\frac{3}{5}$$, find $$\sin \angle BAC$$.
In the answer box, write the fraction in the form a/b.
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