#### Answer

$\theta=22.62^{o}$
$r=13$

#### Work Step by Step

Horizontal and vertical diopters .... are at a right angle,
so the dashed side is a leg of a right triangle and has length 5 .
$(SOHCAHTOA)$
The side opposite to $\theta$ is 5, the side adjacent to it is 12,
$\displaystyle \tan\theta=\frac{5}{12}$
$\displaystyle \theta=\tan^{-1}(\frac{5}{12})\approx$22.619864948$\approx 22.62^{o}$
r is the hypotenuse...Pythagorean theorem:
$r^{2}=5^{2}+12^{2}$
$r^{2}=25+144$
$r^{2}=169$
$r=13$