Mathematics Question and Solution
a² = 6²+8²-2*6*8cos30
a = 4.10628314132 cm.
a = DE.
(4.10628314132/sin30) = (8/sinb)
b = 103.06431342951°
b = Angle ADE.
Angle AED = 180-30-103.06431342951
= 46.93568657049°
tan30 = c/6
c = 3.46410161514 cm.
c = CH.
d = 8-2*3.46410161514
d = 1.07179676972 cm.
e = 1.07179676972+3.46410161514
e = 4.53589838486 cm.
f = atan(6/4.53589838486)
f = 52.91133691903°
g = 90-52.91133691903
g = 37.08866308097°
h = 37.08866308097-30
h = 7.08866308097°
i = 60+46.93568657049
i = 106.93568657049°
j = 180-106.93568657049-7.08866308097
j = 65.97565034854°
(8/sin65.97565034854) = (k/sin7.08866308097)
k = 1.0808744285 cm.
k = EF.
cos30 = 6/l
l = 6.92820323028 cm.
l = BH
m = 8-6.92820323028
m = 1.07179676972 cm.
m = EH
n² = 1.07179676972²+1.0808744285²-2*1.0808744285*1.07179676972cos106.93568657049
n = 1.72972903458 cm.
n = FH.
(1.72972903458/sin106.93568657049) = (1.0808744285/sino)
o = 36.71114966331°
p = 180- 36.71114966331-60
= 83.28885033669°
p = Angle EGH.
(1.07179676972/sin83.28885033669) = (q/sin60)
q = 0.9346072274 cm.
q = GH.
FG = FH-GH
FG = 1.72972903458-0.9346072274
FG = 0.79512180718 cm.
It implies;
FG ÷ GH is;
0.79512180718÷0.9346072274
= 0.85075503791
