Answer
$\phi = 135^{o}$
d = 5.69
c = 12.07
Work Step by Step
The following are the given values:
a = 5
b = 8
$\theta = 45^{o}$
Finding $\phi$:
A parallelogram has a total of $360^{o}$. Using that information:
45 + 45 = 90
360 - 90 = 270
$\frac{270}{2} = 135^{o}$
$\phi = 135^{o}$
Using the Law of Cosines, we can find d:
$d^{2} = 5^{2} + 8^{2} - 2(5)(8)cos(45^{o})$
d = 5.69
Using the Law of Cosines, we can find c:
$c^{2} = 5^{2} + 8^{2} - 2(5)(8)cos(135^{o})$
c = 12.07
In total, the values are:
$\phi = 135^{o}$
d = 5.69
c = 12.07
