Mathematics Question and Solution
Calculating the shaded area.
a² = 4²+6²-2*4*6cos30
a = 3.2296719057 units.
sin15 = b/6
b = 1.5529142706 units.
c = 90-15
c = 75°
Or
cosc = 1.5529142706/6
c = acos(1.5529142706/6)
c = 75°
(3.2296719057/sin30) = (4/sind)
d = 38.2619661994°
e = c-d
e = 75-38.2619661994
e = 36.7380338006°
tan36.7380338006 = f/1.5529142706
f = 1.1591109915 units.
Therefore, area shaded is;
Area triangle with height 1.5529142706 units and base 3.2296719057sin36.7380338006 units - Area triangle with height 1.1591109915 units and base 1.5529142706 units.
= (0.5*1.5529142706*3.2296719057sin36.7380338006)-(0.5*1.1591109915*1.5529142706)
= 1.5-0.9
= 0.6 square units.
= (3/5) square units.
