Mathematics Question and Solution
Calculating r, radius of the circle.
8² = 9²+7²-2*9*7cosa
cosa = (9²+7²-8²)/(2*7*9)
a = acos((9²+7²-8²)/(2*7*9))
a = 58.4118644948°
(8/sin58.4118644948) = (9/sinb)
b = 73.398450401°
c = ½(180-a)
c = ½(180-58.4118644948)
c = 60.7940677526°
d = ½(180-b)
d = ½(180-73.398450401)
d = 53.3007747995°
tan60.7940677526 = r/e
e = r/(tan60.7940677526)
e = 0.5590169944r units.
tan53.3007747995 = r/f
f = r/(tan53.3007747995)
f = 0.7453559925r units.
Therefore, r, radius of the circle is;
e+f = 7
0.5590169944r+0.7453559925r = 7
1.3043729869r = 7
r = 7/1.3043729869
r = 5.366563146 units.
