Mathematics Question and Solution
Calculating D, diameter of the ascribed half circle.
Let r be the radius of the half circle.
a = ½(7)
a = 3.5 units.
b²+a² = r²
b² = r²-3.5²
b = √(r²-12.25) units.
c = 2b
c = 2√(r²-12.25) units.
cosx = 7/(2r) --- (1).
(2√(r²-12.25))² = 2(3²)+2*3*3cosx
4(r²-12.25) = 18+18cosx
4r²-49 = 18+18cosx
4r²-67 = 18cosx
cosx = (4r²-67)/18 --- (2).
Equating (1) and (2).
7/(2r) = (4r²-67)/18
7/r = (4r²-67)/9
Cross Multiply.
63 = 4r³-67r
It implies;
r = 4.5 units.
Therefore, D, diameter of the half circle is;
D = 2r
And r = 4.5 units.
D = 2*4.5
D = 9 units.
