1. **State the problem:** The heights of two poles are in the ratio 9:5. The height of the shorter pole is 8 m. Find the height of the taller pole. 2. **Formula and rules:** If two quantities are in ratio $a:b$, and one quantity is known, the other can be found by setting $a = k \times a'$ and $b = k \times b'$, where $a'$ and $b'$ are the ratio parts and $k$ is a common multiplier. 3. **Set up the equation:** Let the common multiplier be $x$. Then the taller pole's height is $9x$ and the shorter pole's height is $5x$. 4. **Use the known height:** Since the shorter pole is 8 m, we have $$5x = 8$$ 5. **Solve for $x$:** $$x = \frac{8}{5} = 1.6$$ 6. **Find the taller pole's height:** $$9x = 9 \times 1.6 = 14.4$$ 7. **Answer:** The height of the taller pole is **14.4 meters**.