Mathematics Question and Solution
a² = 2*12²-2*12²cos120
a = 12√(3) cm.
a = 20.78460969083 cm.
a = AB.
b = 2a
b = 24√(3) cm.
b = 41.56921938165 cm.
b = AC.
c² = 12²+41.56921938165²-24*41.56921938165cos30
c = 31.74901573277 cm.
c = CO1
(31.74901573277/sin30) = (12/sind)
d = 10.89339464913°
d = Angle O1CA.
e = 180-10.89339464913-30
e = 139.10660535087°
e = Angle AO1C.
f = asin(12/31.74901573277)
f = 22.2076542986°
f = Angle O1CD.
cos22.2076542986 = g/31.74901573277
g = 29.39387691339 cm.
g = CD.
h = 2*10.89339464913
h = 21.78678929826°
h = Angle O1CO2
(31.74901573277/sinh) = (12/sin21.78678929826)
i = 100.8933946492°
i = Angle CEO2.
j = 180-100.8933946492-21.78678929826
j = 57.31981605254°
(k/sin57.31981605254) = (12/sin21.78678929826)
k = 27.21344205665 cm.
k = CE.
It implies;
(DE)² = 27.21344205665²+29.39387691339²-2*29.39387691339*27.21344205665cos22.2076542986
DE = 11.10984119727 cm.
