Math topic, senior three math, how to do 13T, I hope I can give a process, thank you.

Solution: take e as the origin, EF as the x axis, EH as the y axis and EA as the z axis.

Establish a spatial rectangular coordinate system,

Let M(0, b, c), 00≤b≤2, 0≤c≤ 1,

Then g (1, 2,0), f (1, 0,0), h (0 0,2,0),

GM=(- 1，b-2，c)，

GF=(0，-2，0)，

GH=(- 1，0，0)，

cos = 4-2b 2

1+(b-2)2+c2，

cos = 1

1+(b- 1)2+c2，

∠∠MGF =∠MGH，

∴

1+(b-2)2+c2= 1

1+(b- 1)2+c2, the solution is B = 1.

∴

GM=(- 1,-1, c), the normal vector of plane EFG.

N = (0 0,0, 1), and the tangent of the angle between MG and plane EFG is12.

∴|cos|= c

2+c2= 1

From 0≤c≤ 1, the solution is c=

2 2,

∴

GM=(- 1，-2，

2 2),

∴ distance d from point m to plane EFGH d= |

General?

n | |

n|=

2 2.

So the answer is:

2 2.