Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side of the square be 2 units.
(a) Calculating theta, let it be x.
Angle x is;
x+65+90 = 180
x = 180-155
x = 25°
(b) Calculating Area Circle ÷ Area Square to 3 decimal places.
Notice;
Square side is 2 units.
Area square is;
2²
= 4 square units.
Radius of the inscribed circle, r is;
(r/tan35) + (r/tan22.5) = 2
It implies;
r = (2tan22.5*tan35)/(tan22.5+tan35)
r = 0.52051322189 unit.
Area inscribed circle is;
πr²
= π(0.52051322189)²
= 0.8511643085 square units.
Therefore;
Area Circle ÷ Area Square to 3 decimal places is;
0.8511643085 ÷ 4
= 0.21279107713
≈ 0.213
