Answer
$m=\frac{7 \sqrt 3}{3}$
$a= \frac{14\sqrt 3}{3}$
$n=\frac{14\sqrt 3}{3}$
$q=\frac{14\sqrt 6}{3}$
Work Step by Step
The reference triangles provide ratios of the sides. As we start with the hypotenuse of a 30-60-90 triangle, we can determine its other tow sides. After, we use the ratios of a 45-45-90 triangle.
$m=\frac{7}{\sqrt 3}=\frac{7 \sqrt 3}{3}$
$a = 2m$
$a= \frac{14\sqrt 3}{3}$
$a=n=\frac{14\sqrt 3}{3}$
$q=\sqrt 2 n$
$q=\frac{14\sqrt 6}{3}$
