Mathematics Question and Solution
Let alpha be x.
Therefore;
(12/sin2x)=(8/sinx)
And;
Sin2x = 2sinxcosx
Therefore;
(12/2sinxcos)=(8/sinx)
6 = 8cosx
x = acos(6/8)°
2x = 2acos(6/8)°
Let y be the third interior angle.
y = (180-3acos(6/8))°
It implies;
Area of the triangle in cm² is;
Area triangle with height 12 cm and base 8sin(180-3acos(6/8)) cm.
= ½*12*8sin(180-3acos(6/8))
= 48sin(180-3acos(6/8)) cm²
= 39.686269666 cm²
= 39.69 cm² to 2 decimal places.
