Mathematics Question and Solution
Let the side of the regular heptagon be 2 units.
Calculating PH.
AH is;
AH = 2sin(180/7)÷sin(720/7)
AH = 0.89008373583 unit.
AP is;
AP = √(2-2cos(540/7))
AP = 1.24697960372 unit.
Therefore;
PH = AP - AH
= 1.24697960372 - 0.89008373583
PH = 0.35689586789 unit.
Calculating PK.
Notice;
HG = GK
HG is;
HG = 2sin(360/7)÷sin(720/7)
HG = 1.60387547161 unit.
HK is;
HK = √(2(1.60387547161)²-2(1.60387547161)²cos(180/7))
HK = 0.71379173578 unit.
It implies;
PK = HK - PH
= 0.71379173578 - 0.35689586789
PK = 0.35689586789 unit.
Therefore;
0.35689586789 = 0.35689586789
PH = PK
Proved.
