Mathematics Question and Solution
Calculating R, radius of the circle.
Let theta be x.
x+x+x = 360
x = 120°
a² = 6²+5²-2*5*6cos120
a² = 61+30
a = √(91) units.
(√(91)/sin120) = (6/sinb)
b = 33.0044915989°
c² = 5²+15²-2*5*15cos120
c² = 250+75
c = √(325)
c = 5√(13) units.
(5√(13)/sin120) = (15/sind)
d = 46.102113752°
e = b+d
e = 33.0044915989+46.102113752
e = 79.1066053509°
f² = 6²+15²-2*6*15cos120
f² = 261+90
f = √(351)
f = 3√(39) units.
g = ½(f)
g = 1.5√(39) units.
Therefore, R, radius of the circle is;
sin79.1066053509 = (1.5√(39))/R
R = (1.5√(39))/sin79.1066053509
R = 9.53939201417 units.
