Mathematics Question and Solution
a = asin(1/6)
b = 2a
b = 2(asin(1/6))
Where b is angle BAC.
sin(2(asin(1/6))) = c/6
c = ⅓(√(35)) units.
c = 1.97202659437 units.
Where c is BE.
d = 90-2asin(1/6)
d = 70.81186354628°
Where d is angle ABE.
cos70.81186354628 = e/1.97202659437
e = 0.64814814815 unit.
Where e is BD.
tan70.81186354628 = f/0.64814814815
f = 1.86246956135 units.
Where f is DE.
tan(acos(1/6)) = g/0.64814814815
g = 3.83449615572 units.
Where g is DF.
h = 3.83449615572-1.86246956135
h = 1.97202659437 units.
Where h is EF.
⅙ = i/2
i = ⅓ unit.
Where i is CE.
j = 6-⅓
j = ⅓(17) units.
j = 5.66666666667 units.
Where j is AE.
k = 90-2(asin(1/6))
k = 70.81186354628°
Where k is angle AED.
l = 180-70.81186354628
l = 109.18813645372°
Where l is angle AEF.
It implies;
Shaded Area AEF is;
0.5*5.66666666667*1.97202659437sin109.18813645372
= 5.27699709049 square units.
