1. **Problem:** Find the missing side $x$ in the first right-angled triangle where the hypotenuse is 5 cm and the angle adjacent to the base is 27°. 2. **Formula:** Use the sine function since $x$ is opposite the angle 27° and hypotenuse is known. $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply values:** $$\sin(27^\circ) = \frac{x}{5}$$ 4. **Solve for $x$:** $$x = 5 \times \sin(27^\circ)$$ 5. **Calculate:** $$x = 5 \times 0.45399 = 2.26995$$ 6. **Answer:** $x = 2.3$ cm (to 1 decimal place)