Given triangle ABC – rectangular. Angle C = 90 degrees. Angle ADB = 120 degrees. CD = 6. AD = BD. Find AB.
| March 23, 2021 | education
The BDC angle is adjacent to the ADB angle, the sum of which is 180, then the BDC angle = (180 – ADB) = (180 – 120) = 60.
In a right-angled triangle ВСD, the angle DBC = (90 – 60) = 30.
The leg CD lies opposite the angle 30, then BD = 2 * CD = 2 * 6 = 12 cm.
Since, by condition, AD = BD, then triangle ADB is isosceles.
By the cosine theorem in the triangle ADB, we define the length of the side AB.
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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