Mathematics Question and Solution
Let the single side length of the hexagon be 2 units.
Therefore;
AG =√(8-8cos150) units.
Calculating AH.
AH = √((8-8cos150)+4-4√(8-8cos150)cos105)
AH = 4.78834034195 units
Therefore;
MH = ½AH
MH = 2.39417017098 units.
Calculating MG.
MG = √(2.39417017098²+2²-4(2.39417017098)cos51.2060231127)
MG = 1.93185165257 units.
Calculating angle MGH
Let it be x.
x = asin((2.39417017098sin51.2060231127)/1.93185165257)
x = 75°
Therefore;
Angle FGM (angle alpha) is;
90 - angle MGH (x)
= 90-75
= 15°
