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Law of Sines: Difficult Problems with Solutions

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