In triangle ABC, angle B = 120. Find side AB if height AH = 4.
| September 11, 2021 | education
Since the angle ABC is obtuse, the height AH will intersect the side BC on its continuation.
Then the angles ABC and ABH are adjacent, the sum of which is 120, then the angle ABH = 180 – 120 = 60.
In a right-angled triangle ABH Sin60 = AH / AB.
AB = AH / Sin60 = 4 / (√3 / 2) = 8 / √3 = 8 * √3 / 3 cm.
Answer: The length of the AB side is 8 * √3 / 3 cm.
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