Mathematics Question and Solution
Calculating r, radius of the half circle.
a²+14² = (2r)²
a = √(4r²-196) units.
b = (r-2) units.
√(4r²-196)² = 2²+7²-28cosx
4r²-196 = 53+28cosx
28cosx = 4r²-249
cosx = (4r²-249)/28 --- (1).
r² = 7²+(r-2)²-14(r-2)cosx
4r-53 = (28-14r)cosx
cosx = (4r-53)/(28-14r) --- (2).
Calculating r.
Equating (1) and (2).
(4r²-249)/28 = (4r-53)/(28-14r)
28(4r-53) = (28-14r)(4r²-249)
112r-1484 = 112r²-6972-56r³+3486r
56r³-112r²-3374r+5488 = 0
8r³-16r²-482r+784 = 0
4r³-8r²-241r+392 = 0
It implies;
r = 8 units.
