Subjects geography

Position B

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

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.