The beta plane is drawn through the MK side of the MKP equilateral triangle. The distance from the vertex
September 29, 2021 | education
| The beta plane is drawn through the MK side of the MKP equilateral triangle. The distance from the vertex P to this plane is 12 cm. MP = 18 cm Calculate the length of the projection of the median PF onto the plane β (beta)
Since, by condition, the MCR triangle is equilateral, its median is also the height and the bisector.
Then MF = HF = MH / 2 = 18/2 = 9 cm, and triangle MPF is rectangular. Then РF ^ 2 = MP ^ 2 = MF ^ 2 = 324 – 81 = 243.
MP = 8 * √3 cm.
The projection of the median PF onto the plane is the segment OP. The triangle OPF is rectangular, then by the Pythagorean theorem, ОF ^ 2 = PF ^ 2 – OP ^ 2 = 243 – 144 = 99.
ОF = √99 = 3 * √11 cm.
Answer: The length of the projection of the median is 3 * √11 cm.
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