1. **State the problem:** We need to find the measure of angle $\angle B$ in a right triangle with vertices $B$, $C$, and $A$. The side $BC$ is perpendicular to $CA$, so $\angle C$ is the right angle. 2. **Given:** - $BC = 8$ - $CA = 14$ 3. **Identify the sides relative to $\angle B$:** - Opposite side to $\angle B$ is $BC = 8$ - Adjacent side to $\angle B$ is $AB$ (unknown) - Hypotenuse is $CA = 14$ 4. **Use the sine function** because we know the opposite side and hypotenuse: $$\sin(\angle B) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{BC}{CA} = \frac{8}{14}$$ 5. **Simplify the fraction:** $$\sin(\angle B) = \frac{\cancel{8}}{\cancel{14}} = \frac{4}{7}$$ 6. **Calculate $\angle B$ using inverse sine:** $$\angle B = \sin^{-1}\left(\frac{4}{7}\right)$$ 7. **Use a calculator to find the value:** $$\angle B \approx 34.85^\circ$$ 8. **Round to the nearest tenth:** $$\angle B \approx 34.9^\circ$$ **Final answer:** $\boxed{34.9^\circ}$