Angle ABC is 150 °. From point A to line BC, a perpendicular AM is drawn, equal to 12 Find the length of the segment AB.
| May 29, 2021 | education
The magnitude of the expanded angle is 180, then ∠МВА + ∠ABС = 180.
∠МВА + 150 = 180.
∠МВА = 180 – 150 = 30.
Consider a right-angled triangle ABM, in which the leg AM = 12 cm, the angle ∠МВА = 30.
Since the leg AM of a right-angled triangle is located opposite the angle 30, its length is equal to half the length of the hypotenuse AB.
AM = AB / 2.
AB = 2 * AM = 2 * 12 = 24 cm.
Answer: Length AB = 24 cm.
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