Mathematics Question and Solution
Calculating Area of the Circle.
Let a be the radius of the circle.
Calculating a.
a² = 8²+6²-2*8*6(-cosb)
a² = 100+96cosb --- (1).
a² = 8²+16²-2*8*16cosb
a² = 320-256cosb --- (2).
Equating (1) and (2) to get b.
100+96cosb = 320-256cosb
352cosb = 220
b = acos(220/352)
b = 51.3178125465°
Recall.
a² = 320-256cosb at (2).
And b = 51.3178125465°
It implies;
a² = 320-256cos51.3178125465
a = 12.6491106407 units.
Or
Recall again.
a² = 100+96cosb at (1)
And b = 51.3178125465°
It implies;
a² = 100+96cos51.3178125465
a = 12.6491106407 units.
Therefore;
Area circle is;
πa²
= π(12.6491106407)²
= 160π square units.
