1. **State the problem:** We have a right triangle ABC with right angle at A, sides AC = 8 cm, AB = 6 cm, and hypotenuse BC = 10 cm. We need to verify which of the given trigonometric statements are true. 2. **Recall definitions:** - $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$ - $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$ - $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$ 3. **Identify sides relative to angles:** - For angle $C$: - Opposite side = $AB = 6$ cm - Adjacent side = $AC = 8$ cm - Hypotenuse = $BC = 10$ cm - For angle $B$: - Opposite side = $AC = 8$ cm - Adjacent side = $AB = 6$ cm - Hypotenuse = $BC = 10$ cm 4. **Check each statement:** - $\sin C = \frac{8}{10}$? - $\sin C = \frac{\text{opposite to } C}{\text{hypotenuse}} = \frac{6}{10}$, so $\sin C = \frac{6}{10} \neq \frac{8}{10}$ (False) - $\cos B = \frac{6}{10}$? - $\cos B = \frac{\text{adjacent to } B}{\text{hypotenuse}} = \frac{6}{10}$ (True) - $\tan C = \frac{6}{8}$? - $\tan C = \frac{\text{opposite}}{\text{adjacent}} = \frac{6}{8}$ (True) - $\sin B = \cos C$? - $\sin B = \frac{8}{10}$ - $\cos C = \frac{8}{10}$ - So $\sin B = \cos C$ (True) - $\sin B = \frac{6}{10}$? - $\sin B = \frac{8}{10} \neq \frac{6}{10}$ (False) 5. **Final answers:** - True statements: $\cos B = \frac{6}{10}$, $\tan C = \frac{6}{8}$, $\sin B = \cos C$ - False statements: $\sin C = \frac{8}{10}$, $\sin B = \frac{6}{10}$