Question

solve for $x$. round to the nearest tenth, if necessary.
in right triangle $bcd$, right-angled at $c$, hypotenuse $bd = 96$, $angle b = 43^{circ}$, side $dc = x$

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
Here, $\theta=43^\circ$, opposite side $=x$, hypotenuse $=96$.

Step2: Substitute values into formula

$\sin(43^\circ)=\frac{x}{96}$

Step3: Solve for $x$

$x=96\times\sin(43^\circ)$
Calculate $\sin(43^\circ)\approx0.6820$, so $x\approx96\times0.6820$

Step4: Compute final value

$x\approx65.472$
Round to nearest tenth: $x\approx65.5$

Answer:

$65.5$