1. **State the problem:** We have point A at coordinates (70S, 105W). Point B is located 30 degrees due south of A. We need to find the coordinates of B.
2. **Understand the coordinates:** Latitude is given as 70S, which means 70 degrees south of the equator. Longitude is 105W, which means 105 degrees west of the prime meridian.
3. **Moving due south:** Moving 30 degrees due south from 70S means increasing the latitude by 30 degrees towards the South Pole.
4. **Calculate the new latitude:**
$$\text{Latitude of B} = 70^\circ S + 30^\circ = 100^\circ S$$
5. **Check latitude bounds:** Latitude ranges from 0° at the equator to 90° at the poles. 100°S is beyond the South Pole, so we must reflect it:
$$100^\circ S = 90^\circ S + 10^\circ = 10^\circ N$$
This means after crossing the South Pole, the latitude is 10° north.
6. **Adjust longitude after crossing the pole:** When crossing the pole, longitude changes by 180°:
$$\text{Longitude of B} = 105^\circ W + 180^\circ = 285^\circ$$
Since longitude is usually expressed between 0° and 180° east or west, convert 285°:
$$285^\circ = 360^\circ - 285^\circ = 75^\circ E$$
7. **Final coordinates of B:**
$$B = (10^\circ N, 75^\circ E)$$
**Answer:** The position of B is 10 degrees north latitude and 75 degrees east longitude.
Position B
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