1. **State the problem:** We have a right-angled triangle ABC with the right angle at B. The hypotenuse AC is 15 cm, and angle BAC is 38°. We need to find the length of side BC. 2. **Identify the sides relative to angle BAC:** - Hypotenuse (AC) = 15 cm - Angle BAC = 38° - Side BC is opposite angle BAC 3. **Formula used:** In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 4. **Apply the formula:** $$\sin(38^\circ) = \frac{BC}{15}$$ 5. **Solve for BC:** $$BC = 15 \times \sin(38^\circ)$$ 6. **Calculate the value:** Using a calculator, $$\sin(38^\circ) \approx 0.6157$$ So, $$BC = 15 \times 0.6157 = 9.2355$$ 7. **Final answer:** $$BC \approx 9.24 \text{ cm}$$ Thus, the length of side BC is approximately 9.24 cm.