The beta plane is drawn through the MK side of the MKP equilateral triangle. The distance from the vertex

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.