Answer
$ L = \frac{6}{cos\theta} + \frac{6}{sin\theta}$
Work Step by Step
We find each individual lengths. (In order to do this problem, you must remember that vertical angles are congruent.) Thus, we find:
$sin \theta = \frac{6}{l_1} \\ l_1 =\frac{6}{sin \theta } $
And:
$cos \theta = \frac{6}{l_2} \\ l_2 =\frac{6}{cos \theta } $
L is equal to $l_1$ plus $l_2$, so we find:
$ L = \frac{6}{cos\theta} + \frac{6}{sin\theta}$
