Mathematics Question and Solution
Calculating length x.
5² = 8²+7²-2*8*7cosa
112cosa = 64+49-25
cosa = 88/112
a = acos(88/112)
a = 38.2132107017°
a is the angle opposite 5 units.
(5/sin38.2132107017) = (7/sinb)
b = 60°
b is the angle opposite 7 units.
c = 2a
c = 2*38.2132107017
c = 76.4264214034°
sin38.2132107017 = (0.5*5)/d
d = 4.0414518843 units.
d is the radius of the circle.
e = ½(180-76.4264214034)
e = 51.7867892983°
f = e-0.5b
f = 51.7867892983-0.5*60
f = 21.7867892983°
cos21.7867892983 = g/4.0414518843
g = 3.7527767497 units.
h = 2g
h = 7.5055534994 units.
It implies, x the required length is;
x² = 7.5055534994²+5²-7.5055534994*2*5cos30
x = 4.0414518843 units.
Notice!
x, 4.0414518843 units is also d, the radius of the circle.
