In triangle ABC BC = 12, sinA = 2/3, outside angle at vertex C is 150. Find AB
| September 27, 2021 | education
The angle ACB of the triangle ACB and the outer angle BCD are adjacent angles, the sum of which is 180, then the angle ACB = 180 – BCD = 180 – 150 = 30.
By the sine theorem, the sides of a triangle are proportional to the opposite angles.
Then AB / SinBCA = BC / SinBAC.
AB / (1/2) = 12 / (2/3).
AB = (36/2) * (1/2) = 36/4 = 9 cm.
Answer: The length of the AB side is 9 cm.
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