1. **State the problem:** We have a telephone wire stretched from the top of a telephone pole to a stake in the ground. The wire length is 7 metres, and the horizontal distance from the pole to the stake is 2 metres. We need to find the height of the telephone pole. 2. **Formula used:** This is a right triangle problem where the wire is the hypotenuse ($c$), the horizontal distance is one leg ($a$), and the pole height is the other leg ($b$). Pythagoras' theorem states: $$c^2 = a^2 + b^2$$ 3. **Identify known values:** - Hypotenuse $c = 7$ - One leg $a = 2$ - Unknown leg $b$ (height of the pole) 4. **Apply the formula:** $$7^2 = 2^2 + b^2$$ $$49 = 4 + b^2$$ 5. **Solve for $b^2$:** $$b^2 = 49 - 4 = 45$$ 6. **Find $b$ by taking the square root:** $$b = \sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5} \approx 6.7$$ 7. **Answer:** The telephone pole is approximately **6.7 metres** tall when rounded to the nearest tenth.