Final answer:
The question requires using trigonometry to find the displacement vector representing the distance to base camp the explorer must now travel after being off-course. This involves calculating the north and east components of the explorer's actual path, then determining the discrepancy with the intended path.
Step-by-step explanation:
The student's question involves finding the distance the explorer must now travel to reach the base camp, given that he unintentionally traveled 7.8 km at 49° north of due east, while he was supposed to travel due north for 4.4 km. This is a problem of vector addition and can be solved using trigonometry.
We can treat the intended and actual paths as vectors, where the intended path is 4.4 km due north, and the actual path is 7.8 km at 49° north of due east. Using a right triangle, we can determine the north-south and east-west components of the actual travel path. The north component (N) can be found using cosine(49°), and the east component (E) using sine(49°).
To find how far the explorer is from the base camp after the whiteout, we need to determine the discrepancy between where he is and where he intended to be, which can be represented by a displacement vector from his current location to the base camp. This new displacement vector can be calculated by subtracting the north component of his travel from the intended 4.4 km and taking into account the eastward displacement. The magnitude of this vector gives us the straight-line distance he must now travel to the base camp.
Using the Pythagorean theorem, we calculate the magnitude of this displacement vector, which will be the distance to base camp. The direction can then be determined with respect to either north or east, using trigonometric functions such as arctangent.