20)
Given two sides of a triangle and the angle corresponding the the third side, the formula for calculating the area is
Area = 1/2 x product of the two sides x Sine of the given angle
From the information given,
Area = D
angle = C
the other sides are a and b
By applying the formula, we have
D = 1/2 x a x b x Sin C
D = 1/2 x abSinC
By multiplying both sides of the equation by 2,
d * 2 = 2 * 1/2 * abSinC
2D = abSinC
Dividing both sides of the equation by ab, we have
2D/ab = abSinC/ab
2D/ab = Sin C
Taking the sin inverse of 2D/ab, we have
C = Sin^-1(2D/ab)