Question: A length of wire is connected from the top of a 7 m telegraph pole to a point 3 m away from the base, as shown below.
Use Pythagoras' theorem to find the length of the wire, $n$.
Give your answer to 1 d.p.
1. **State the problem:** We need to find the length of the wire $n$ that connects the top of a telegraph pole to a point 3 m from its base.
2. **Identify the shape and theorem:** The wire, pole, and ground form a right triangle with vertical side 7 m, horizontal side 3 m, and hypotenuse $n$.
3. **Formula:** By Pythagoras' theorem, $$n^2 = 7^2 + 3^2$$
4. **Calculate squares:** $$n^2 = 49 + 9$$
5. **Sum:** $$n^2 = 58$$
6. **Find $n$ by taking the square root:** $$n = \sqrt{58}$$
7. **Approximate:** $$n \approx 7.6157$$
8. **Round to 1 decimal place:** $$n \approx 7.6$$
**Final answer:** The length of the wire is approximately $7.6$ meters.