Answer
Both sides of the equation in Mollweide's formula are equal, which verifies the accuracy of the information given in the question.
Work Step by Step
$a = 7$
$b = 7\sqrt{3}$
$c = 14$
$A = 30^{\circ}$
$B = 60^{\circ}$
$C = 90^{\circ}$
We can find the value of the left side of Mollweide's formula:
$\frac{a-b}{c} = \frac{7-7\sqrt{3}}{14} = -0.366$
We can find the value of the right side of Mollweide's formula:
$\frac{sin~\frac{1}{2}(A-B)}{cos~\frac{1}{2}C} = \frac{sin~\frac{1}{2}(30^{\circ}-60^{\circ})}{cos~\frac{1}{2}90^{\circ}}$
$\frac{sin~\frac{1}{2}(A-B)}{cos~\frac{1}{2}C} = \frac{sin~\frac{1}{2}(-30^{\circ})}{cos~45^{\circ}}$
$\frac{sin~\frac{1}{2}(A-B)}{cos~\frac{1}{2}C} = \frac{sin~(-15^{\circ})}{cos~45^{\circ}}$
$\frac{sin~\frac{1}{2}(A-B)}{cos~\frac{1}{2}C} = -0.366$
Both sides of the equation in Mollweide's formula are equal, which verifies the accuracy of the information given in the question.