Chapter 1 - Trigonometric Functions - Section 1.2 Angle Relationships and Similar Triangles - 1.2 Exercises - Page 18: 54

$a=2$

1. First we need to find our ratios setting up two similar sides of the triangle. In this case, we know both hypotenuses, we will use them. It is better to reduce the ratio if it is possible $\frac{3}{9}=\frac{1}{3}$ 2. Make following three equivalent ratios $\frac{1}{3} =\frac{a}{6}$ 3. We need find a by solving the equation $\frac{1}{3} =\frac{a}{6}$ $3a=6$ $a=2$