In parallelogram ABCD, AB = 20cm. angle BAD = 45. BM is perpendicular to the ABC plane.
| February 9, 2021 | education
In parallelogram ABCD, AB = 20cm. angle BAD = 45. BM is perpendicular to the ABC plane. The angle between straight line MA and plane ABC = 60. Find the distance from M to ABC
Since, by condition, ВM is perpendicular to the plane ABC, then triangle ABM is rectangular.
Determine the value of the angle AMB. Angle AMB = (180 – 90 – 60) = 30, then the leg AB is located opposite the angle 300, which means AM = 2 * AB = 2 * 20 = 40 cm.
By the Pythagorean theorem, we determine the length of the leg BM.
BM ^ 2 = AM ^ 2 – AB ^ 2 = 1600 – 400 = 120.
ВM = √1200 = 20 * √3 cm.
Answer: From point M to plane 20 * √3 cm.
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