Question

sine law and cosine law
given the triangle, find the length of side $x$ using the law of sines. round your final answer to 4 decimal places.
$x=$

Explanation:

Step1: Recall Law of Sines formula

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. In our triangle, if the side of length 12 is opposite the $47^{\circ}$ - angle and side $x$ is opposite the $26^{\circ}$ - angle, then $\frac{x}{\sin26^{\circ}}=\frac{12}{\sin47^{\circ}}$.

Step2: Solve for $x$

We can cross - multiply to get $x=\frac{12\times\sin26^{\circ}}{\sin47^{\circ}}$.
We know that $\sin26^{\circ}\approx0.4384$ and $\sin47^{\circ}\approx0.7314$.
Then $x=\frac{12\times0.4384}{0.7314}=\frac{5.2608}{0.7314}\approx7.1928$.

Answer:

$7.1928$