Question

bc =
round your answer to the nearest hundredth.

Explanation:

Step1: Identify adjacent side

In right $\triangle ABC$, $\angle B=35^\circ$, hypotenuse $AB=6$. $BC$ is adjacent to $\angle B$.

Step2: Use cosine definition

Cosine: $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(35^\circ)=\frac{BC}{AB}$

Step3: Solve for $BC$

Rearrange to isolate $BC$:
$BC = AB \times \cos(35^\circ)$
Substitute values:
$BC = 6 \times \cos(35^\circ)$
Calculate $\cos(35^\circ)\approx0.8192$, so:
$BC \approx 6 \times 0.8192$

Step4: Compute final value

$BC \approx 4.9152$
Round to nearest hundredth.

Answer:

$4.92$