Mathematics Question and Solution
Calculating PQ.
a = 8+2
a = 10 cm.
a is the diameter, AC of the semi circle.
b = ½(AC)
b = ½(10)
b = 5 cm.
b is the radius of the semi circle.
c = b-2
c = 5-2
c = 3 cm.
5² = 3²+d²
d² = 25-9
d = √(16)
d = 4 cm.
d is the radius of the circle.
4² = 5²+5²-2*5*5cose
50cose = 50-16
cose = (34/50)
e = acos(17/25)°
f = 2e
f = 2acos(17/25)°
It implies;
Length PQ is;
(PQ)² = 5²+5²-2*5*5cos(2acos(17/25))
(PQ)² = 50-50cos(2acos(17/25))
(PQ)² = 53.76
PQ = √(53.76)
PQ = 7.3321211119 cm.
PQ = 7.33 cm to 2 decimal places.
