Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let CD = 1 unit.
Therefore;
AB = 2 units.
(a) Calculating Alpha, let it be y to 2 decimal places.
(0.84523652348/siny) = (1/sin115)
siny = 0.84523652348sin115
y = asin(0.84523652348sin115)
y = 49.99999999989°
≈ 50°
(b) Calculating Area Hexagon ÷ Area Green to 2 decimal places.
Let the side of the regular hexagon be x.
Calculating x.
2x = 2.09302817926
Where 2.09302817926 units is the vertical length from A to the apex (vertical length of symmetry) of the regular hexagon.
It implies;
x = 1.04651408963 units.
Area Regular Hexagon is;
½(6* 1.04651408963 )(1.04651408963/(2tan(180/6))
= (3*1.04651408963)*0.5( 1.04651408963*√(3))
= 2.84539160603 square units.
Area Green is;
Area triangle with height 0.84523652348 unit and base sin15 units.
= ½*0.84523652348sin15
= 0.10938165495 square units.
It implies;
Area Hexagon ÷ Area Green to 2 decimal places is;
2.84539160603 ÷ 0.10938165495
= 26.01342617666
≈ 26.01
