Area of Triangles

Area of Triangles - Sine Rule


In triangle ABC,ABC, AB=3,AB=3, AC=12,AC = 12, and sinBAC=0.5.\sin \angle BAC = 0.5. What is the area of triangle ABC?ABC?

In ABC,\triangle ABC, AC=3AC = 3 and sinACB=23.\sin \angle ACB = \frac{2}{3}. If the area of ABC\triangle ABC is 9,9, what is BC?BC?

In triangle ABCABC above, AD\overline{AD} bisects BC.\overline{BC}. Given that AB=12,AB = 12, AD=8,AD =8, and sinBAD=14,\sin \angle BAD = \frac{1}{4}, what is the area of ABC?\triangle ABC?

In triangle ABC,ABC, AD\overline{AD} bisects BAC,\angle BAC, AE\overline{AE} is perpendicular to BC,\overline{BC}, and FF and GG are the midpoints of AB\overline{AB} and AC,\overline{AC}, respectively. Given that AB=16,AB = 16, AC=13,AC=13, AH=13,AH=13, and AI=8,AI=8, and BAC=90,\angle BAC = 90^{\circ}, which of the following triangles has an area equal to half the area of ABC?\triangle ABC?

In triangle ABC,ABC, AB=3AB = 3 and BC=6.BC=6. If the area of the triangle is 6,6, what is sinABC?\sin \angle ABC?


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