1. Problem: In the right triangle with right angle at C, the hypotenuse AB = 12 cm and angle A = $25^\circ$, and side BC is $a$, find $a$.\n2. Formula and rules: For right triangles use the sine ratio, $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$.\nAlways use degree mode for the calculator because the angle is given in degrees.\n3. Setup: Using angle A, the side opposite is $a$ and the hypotenuse is 12, so $$\sin(25^\circ)=\frac{a}{12}$$.\n4. Solve: Multiply both sides by 12 to isolate $a$, giving $$a=12\sin(25^\circ)$$.\n5. Evaluate: Compute in degree mode $12\sin(25^\circ)\approx 12\times 0.4226182617=5.0714191404$, which rounds to $5$ (nearest whole number).\n6. Final answer: $a\approx 5$ cm.\n