In triangle ABC, the angle C is 90, the sine of the outer angle at the vertex A is 0.5, BC = 4. Find AB.
| January 14, 2021 | education
The outer corner of the BAD and the inner corner of the BAC are adjacent angles, the sum of which is 180.
Then the angle BAC = (180 – ВAD), and therefore, SinBAC = Sin (180 – BAD) = SinВAD = 0.5.
Then in a right-angled triangle ABC SinBAC = BA / AB.
AB = BA / SinBAC = 4 / 0.5 = 8 cm.
Answer: The length of the hypotenuse AB is 8 cm.
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