Question

round to the nearest tenth when necessary. 1 fill in the blank 1 point

Explanation:

Step1: Find the third - angle of the triangle

The sum of angles in a triangle is $180^{\circ}$. Let the third - angle be $y$. So, $y=180^{\circ}-126^{\circ}-33^{\circ}=21^{\circ}$.

Step2: Use the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. Here, we have $\frac{x}{\sin126^{\circ}}=\frac{8}{\sin21^{\circ}}$.

Step3: Solve for $x$

Cross - multiply to get $x=\frac{8\times\sin126^{\circ}}{\sin21^{\circ}}$. Since $\sin126^{\circ}\approx0.809$ and $\sin21^{\circ}\approx0.358$, then $x=\frac{8\times0.809}{0.358}=\frac{6.472}{0.358}\approx18.1$.

Answer:

$18.1$