Question: a helicopter is flying from redville to leek. the helicopter departs redville, flies $60$ miles west, then $25$ miles north and arrives in leek. work out the distrance of leek from redville
1. **State the problem:**
A helicopter flies $60$ miles west and then $25$ miles north from Redville to Leek. We need to find the straight-line distance from Redville to Leek.
2. **Formula used:**
We use the Pythagorean theorem for right-angled triangles:
$$d = \sqrt{a^2 + b^2}$$
where $a$ and $b$ are the legs of the triangle, and $d$ is the hypotenuse (the straight-line distance).
3. **Identify the legs:**
Here, $a = 60$ miles (west), $b = 25$ miles (north).
4. **Calculate the distance:**
$$d = \sqrt{60^2 + 25^2} = \sqrt{3600 + 625} = \sqrt{4225}$$
5. **Simplify the square root:**
$$d = 65$$
6. **Answer:**
The distance from Redville to Leek is $65$ miles.