1. **State the problem:** We have a right-angled triangle with hypotenuse 8.6 cm, base 6.9 cm, and height $x$ cm. We need to find $x$ correct to 3 significant figures. 2. **Formula used:** In a right-angled triangle, by Pythagoras' theorem: $$\text{hypotenuse}^2 = \text{base}^2 + \text{height}^2$$ 3. **Apply the formula:** $$8.6^2 = 6.9^2 + x^2$$ 4. **Calculate squares:** $$73.96 = 47.61 + x^2$$ 5. **Isolate $x^2$:** $$x^2 = 73.96 - 47.61$$ $$x^2 = 26.35$$ 6. **Find $x$ by taking the square root:** $$x = \sqrt{26.35}$$ 7. **Calculate the square root:** $$x \approx 5.13$$ 8. **Answer:** The height $x$ is approximately **5.13 cm** to 3 significant figures.