Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Use sine function

In right - triangle BCD, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 43^{\circ}$, the opposite side to $\angle B$ is $x$ and the hypotenuse is 96. So $\sin43^{\circ}=\frac{x}{96}$.

Step2: Solve for $x$

Multiply both sides of the equation $\sin43^{\circ}=\frac{x}{96}$ by 96. We get $x = 96\times\sin43^{\circ}$. Since $\sin43^{\circ}\approx0.682$, then $x=96\times0.682 = 65.5$.

Answer:

$65.5$