find the number that belongs in the green box. round your answer to the nearest tenth.

Explanation:

Step1: Find the third - angle

The sum of angles in a triangle is 180°. Let the third - angle be $x$. Then $x=180-(70 + 55)=55^{\circ}$.

Step2: Use the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. Let the side opposite the 70° angle be $a$ (the side we want to find), the side opposite the 55° angle be $b = 14$, and the side opposite the other 55° angle be $c = 16.1$. Using $\frac{a}{\sin70^{\circ}}=\frac{14}{\sin55^{\circ}}$. We can solve for $a$: $a=\frac{14\sin70^{\circ}}{\sin55^{\circ}}$. We know that $\sin70^{\circ}\approx0.9397$ and $\sin55^{\circ}\approx0.8192$. $a=\frac{14\times0.9397}{0.8192}=\frac{13.1558}{0.8192}\approx16.1$.

Answer:

$16.1$