Mathematics Question and Solution
Calculating Angle Theta.
Let theta be a, angle CAD.
b = 180-40-80
b = 60°
b is angle BCD.
Let X = 1 unit.
X is BD.
(1/sin60) = (Y/sin80)
Y = 1.1371580426 units.
Y is BC.
(c/sin40) = (1/sin60)
c = 0.74222719897 units.
c is CD.
It implies;
X+Y = 1+1.1371580426
X+Y = 2.1371580426 units.
X+Y is AC.
d = 180-80
d = 100°
d is angle ADC.
Therefore;
Calculating theta, a (angle CAD).
((X+Y)/sind) = (c/sina)
(2.1371580426/sin100) = (0.74222719897/sina)
sina = (0.74222719897sin100)/(2.1371580426)
a = asin((0.74222719897)/(2.1371580426))
a = asin(0.34202014333)
a = 20°
Again, a is theta, angle CAD.
