Mathematics Question and Solution
sin15 = a/6
a = 1.5529142706 units.
a is CD.
cos15 = b/6
b = 5.7955549577 units.
b is BD.
c² = 4²+6²-2*4*6cos30
c = 3.2296719057 units.
c is AC.
(3.2296719057/sin30) = (4/sind)
d = 38.2619661997°
d is angle ACB.
e = (90-15)-d
e = 75-38.2619661997
e = 36.7380338003°
e is angle ACD.
tan36.7380338003 = f/1.5529142706
f = 1.1591109915 units.
f is DE.
Therefore, area triangle ADE is;
Area triangle with height 3.2296719057 units and base 1.5529142706sin36.7380338003 units - Area triangle with height 1.1591109915 units and base 1.5529142706 units.
= 0.5*3.2296719057*1.5529142706sin36.7380338003-0.5*1.5529142706*1.1591109915
= 1.5-0.9
= 0.6 square units.
= ⅗ square units.
