Question

use the law of sines to find the indicated side x. (assume a = 11. round your answer to one decimal place.) x =

Explanation:

Step1: Recall Law of Sines

The Law of Sines states that $\frac{x}{\sin B}=\frac{a}{\sin A}$.

Step2: Substitute given values

We know $A = 37.5^{\circ}$, $B=28.1^{\circ}$ and $a = 11$. So $x=\frac{a\sin B}{\sin A}$.

Step3: Calculate x

$x=\frac{11\times\sin(28.1^{\circ})}{\sin(37.5^{\circ})}$. First, $\sin(28.1^{\circ})\approx0.471$ and $\sin(37.5^{\circ})\approx0.609$. Then $x=\frac{11\times0.471}{0.609}=\frac{5.181}{0.609}\approx8.5$.

Answer:

$8.5$