1. **State the problem:** We have a right triangle with one leg measuring 8.7 cm, the hypotenuse measuring 8.9 cm, and the other leg labeled as $a$. We need to find the length of the missing leg $a$. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs and $c$ is the hypotenuse. 3. **Apply the formula:** Here, $b = 8.7$ cm and $c = 8.9$ cm. Substitute these values: $$a^2 + 8.7^2 = 8.9^2$$ 4. **Calculate squares:** $$a^2 + 75.69 = 79.21$$ 5. **Isolate $a^2$:** $$a^2 = 79.21 - 75.69$$ $$a^2 = 3.52$$ 6. **Find $a$ by taking the square root:** $$a = \sqrt{3.52}$$ 7. **Calculate the square root:** $$a \approx 1.876$$ 8. **Round to the nearest tenth:** $$a \approx 1.9$$ centimeters **Final answer:** The length of the missing leg $a$ is approximately 1.9 centimeters.