Mathematics Question and Solution
Calculating r, radius of the circle.
(r/tan40)+(r/tan30) = 10
r = 3.42020143326 cm.
(a/sin60) = (10/sin40)
a = 13.47296355334 cm.
tan40 = 3.42020143326/b
b = 4.07603734548
(4.07603734548/sin50) = (c/sin80)
c = 5.24005260459 cm.
d = 13.47296355334-4.07603734548
d = 9.39692620786 cm.
e² = 9.39692620786²+5.24005260459²-2*9.39692620786*5.24005260459cos130
e = 13.38142726359 cm.
(13.38142726359/sin130) = (5.24005260459/sinf)
f = 17.45618925878°
g = 100-17.45618925878
g = 82.54381074122°
tan30 = 3.42020143326/h
h = 5.92396265453 cm.
i² = 5.92396265453²+10²-20*5.92396265453cos60
i = 8.70940336573 cm.
(8.70940336573/sin60) = (5.92396265453/sinj)
j = 36.0898510019°
k = 180-j-g
k = 61.36633825688°
l = 10-5.92396265453
l = 4.07603734547 cm.
(m/sin36.0898510019) = (4.07603734547/sin61.36633825688)
m = 2.73555725483 cm.
n = 90-82.54381074122
n = 7.45618925878°
o² = 2.73555725483²+3.42020143326²-2*3.42020143326*2.73555725483cos7.45618925878
o = 0.79180926716 cm
(0.79180926716/sin7.45618925878) = (2.73555725483/sinp)
p = 26.6362725882°
q = 60-p
q = 33.3637274118°
cos33.3637274118 = 3.42020143326/s
s = 4.09508743629 cm.
t = s+0.79180926716
t = 4.88689670345 cm.
u = 13.38142726359-2.73555725483
u = 10.64587000876 cm.
v = 7.45618925878+26.6362725882
v = 34.09246184698°
Therefore;
Area Green in cm² to 1 decimal place is;
0.5*4.88689670345*10.64587000876sin34.09246184698
= 14.58086265276 cm²
≈ 14.6 cm²
