Triangle ABC-rectangular corner ADB = 120, CD = 6? Find AB
| March 20, 2021 | education
The ADC angle is adjacent to the ADB angle, the sum of which is 180, then the ADC angle = (180 – ADB) = (180 – 120) = 60.
In a right-angled triangle ACD, the angle CAD = (90 – 60) = 30.
The leg CD lies against an angle of 30, then AD = 2 * CD = 2 * 6 = 12 cm.
Then ВD = AD = 12 cm.
In triangle ADB, by the cosine theorem:
AB ^ 2 = AD ^ 2 + BD ^ 2 – 2 * AD * BD * Cos120 = 144 + 144 – 2 * 12 * 12 (-1/2) = 3 * 144.
AB = 12 * √3 cm.
Answer: The length of the AB side is 12 * √3 cm.
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