Question

what is the length of $overline{bc}$? round to the nearest tenth.

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$, where $\theta=65^\circ$, opposite side is $BC=x$, hypotenuse $AB=16$ cm.

Step2: Substitute values into formula

$\sin(65^\circ)=\frac{x}{16}$

Step3: Solve for $x$

$x=16\times\sin(65^\circ)$
Calculate $\sin(65^\circ)\approx0.9063$, so $x\approx16\times0.9063$

Step4: Compute final value

$x\approx14.5008$
Round to nearest tenth: $x\approx14.5$

Answer:

14.5 cm