Mathematics Question and Solution
Radius of the semi circle is 12 cm.
Angle AED = atan(½)°
sin(atan½) = a/24
a = 10.733126292 cm.
a = AF.
cos(atan½) = b/12
b = 21.466252584 cm.
b = EF.
cos(atan2) = c/10.733126292
c = 4.8 cm.
d = 12-4.8
d = 7.2 cm.
e² = 7.2²+6²
e = 9.37229961109 cm.
f = atan(6/7.2)
f = 39.80557109227°
(12/sin39.80557109227) = (7.2/sing)
g = 22.58853878798°
h = 180-22.58853878798-39.80557109227
h = 117.60589011975°
(i/sin117.60589011975) = (12/sin39.80557109227)
i = 16.61063807106 cm.
j = 16.61063807106-9.37229961109
j = 7.23833845997 cm.
k² = 12²+6²
k = 13.416407865 cm.
l = 21.466252584-13.416407865
l = 8.049844719 cm.
m = atan(2)+atan(7.2/6)
m = 113.62937773066°
n² = 7.23833845997+8.049844719-2*7.23833845997*8.049844719cos113.62937773066
n = 12.8024594116 cm.
n = FG.
(12.8024594116/sin113.62937773066) = (8.049844719/sino)
o = 35.17356732924°
p = 180-35.17356732924-113.62937773066
p = 31.1970549401°
q = 180-31.1970549401-atan(2)
q = 85.36799623698°
(8.049844719/sin85.36799623698) = (r/sin(atan2)
r = 7.21301295216 cm.
r = FH.
GH = 12.8024594116-7.21301295216
GH = 5.58944645944 cm.
It implies;
FH ÷ GH is;
7.21301295216÷5.58944645944
= 1.29046999636
