Mathematics Question and Solution
sin30 = a/10
a = 5 cm.
b = 10+2a
b = 20 cm.
c² = 20²+4²-160cos60
c = 4√(21) cm.
c = 18.3303027798 cm.
(18.3303027798/sin60) = (20/sind)
d = asin(5√(7)/14)°
d = 70.8933946491°
e = 180-d
e = (180-asin(5√(7)/14))°
e = 109.1066053509°
Where e is x.
Therefore;
tanx is;
tan(180-asin(5√(7)/14))
tan(109.1066053509)
= -2.8867513459
Calculating Blue Area.
f² = 10²+10²-200cos 120
f = 10√(3) cm.
g² = 10²+4²-2*10*4cos120
g = 2√(39) cm.
(2√(39)/sin120) = (10/sinh)
h = asin(5√(13)/26)°
h = 43.897886248°
j = 180-asin(5√(7)/14)-asin(5√(13)/26)
j = 65.2087191029°
sin65.2087191029 = k/(2√(39))
k = 11.3389341903 cm.
l = 90-65.2087191029
l = 24.7912808971°
m = 60-43.897886248
m = 16.102113752°
n = 24.7912808971+16.102113752-30
n = 10.8933946491°
o = 90-10.8933946491
o = 79.1066053509°
tan79.1066053509 = 10√(3)/p
p = ½(10) cm.
sin79.1066053509 = 10√(3)/q
q = 17.6383420738 cm.
r = 17.6383420738-11.3389341903
r = 6.2994078835 cm.
Therefore;
Area Blue exactly in decimal is;
0.5*(10/3)*6.2994078835sin79.1066053509
= 10.3098262355 cm²
It implies;
tanx is;
tan(180-asin(5√(7)/14))
= tan(109.1066053509)
= -2.8867513459
Area Blue is;
= 10.3098262355 cm² exactly in decimal.
