Answer
$\phi = 111.80^{o}$
$\theta = 68.20$
d = 13.86
Work Step by Step
The following are the given values:
a = 10
b = 14
c = 20
Using the Law of Cosines, we can find $\phi$:
$cos(\phi) = \frac{10^{2} + 14^{2} - 20^{2}}{2(10)(14)}$
$\phi = 111.80^{o}$
Knowing that a parallelogram has $360^{o}$, we can find $\theta$:
$\frac{360 - (111.80)(2)}{2} = 68.20$
$\theta = 68.20$
Using the Law of Cosines, we can find d:
$d^{2} = 10^{2} + 14^{2} - 2(10)(14)cos(68.20^{o})$
d = 13.86
$\phi = 111.80^{o}$
$\theta = 68.20$
d = 13.86
