Mathematics Question and Solution
Calculating x (AD) the diameter of the half circle.
a² = 2²+11²+2*2*11cosy
a² = 125+44cosy --- (1).
a² = x²+7²-2*7*xcosy
a² = x²+49-14xcosy --- (2).
Where a is AC.
cosy = 7/x --- (3).
Equating (1) and (2).
125+44cosy = x²+49-14xcosy
76 = x²-14xcosy-44cosy --- (4).
Calculating x.
Substituting (3) in (4).
76 = x²-14x(7/x)-44(7/x)
76 = x²-98-(308/x)
174 = x²-(308/x)
174x = x³-308
x³-174x = 308
It implies;
x = 14 cm.
