Mathematics Question and Solution
sin45 = 12/a
a = 12√(2) cm.
a is AC.
Notice !
AB = 2BC
Let BC = b
Therefore;
AB = 2b cm.
AC = AB+BC
AC = 2b+b
AC = 3b cm.
And AC = 12√(2) cm.
It implies;
12√(2) = 3b
b = 4√(2) cm.
Again, b is BC.
AB = 2b
And b is 4√(2) cm.
AB = 2*4√(2)
AB = 8√(2) cm.
c = 180-30-45
c = 105°
(12/sin105) = (d/sin30)
d = (6/sin105) cm.
d = 6.2116570825 cm.
e = 8√(2)-d
e = (8√(2)sin105-6)/sin105 cm.
e = 5.1020514165 cm
(((8√(2)sin105-6)/sin105)
/sin30) = (f/sin105)
f = (4√(2)sin105-3) cm.
f = 9.8564064606 cm.
f is the side length of the regular triangle.
g = 180-60-45
g = 75°
Therefore, Green Area exactly in decimal is;
(0.5*6.2116570825*12sin45)+(0.5*9.8564064606*5.6568542495sin75)
= 53.2820323031 cm²
