1. **State the problem:** We have a right triangle with a height of $\frac{5}{3}$ meters and we need to find the base length $b$ meters. 2. **Identify the known information:** The height (opposite side) is $\frac{5}{3}$ m. The triangle is right-angled, so we can use the Pythagorean theorem if the hypotenuse or another side is known. However, since only the height and the hypotenuse are mentioned, we assume the hypotenuse is given or implied. 3. **Formula used:** The Pythagorean theorem states: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs of the right triangle and $c$ is the hypotenuse. 4. **Assuming the hypotenuse length is known or given as $c$, we solve for $b$:** $$b = \sqrt{c^2 - a^2}$$ 5. **Since the hypotenuse length is not provided, we cannot calculate $b$ exactly without it.** 6. **If the hypotenuse length $c$ is given, plug in the values:** $$b = \sqrt{c^2 - \left(\frac{5}{3}\right)^2} = \sqrt{c^2 - \frac{25}{9}}$$ 7. **Without the hypotenuse length, the base $b$ cannot be determined.** **Final answer:** $b = \sqrt{c^2 - \frac{25}{9}}$ meters, where $c$ is the hypotenuse length.