Here is how to solve this problem:
Understanding the Problem
* Direction: The reindeer moves 45 degrees east of south. This means it is moving in a direction that is 45 degrees to the right of a straight southward direction.
* Distance: We need to find the total distance traveled, which is the length of the reindeer's path.
Solving the Problem
1. Visualize: Imagine a right triangle where:
* The hypotenuse represents the reindeer's path.
* The vertical side represents the southward component of the reindeer's movement.
* The horizontal side represents the eastward component of the reindeer's movement.
2. Trigonometry: Since we have the angle (45 degrees) and we want to find the hypotenuse, we will use the sine function:
* sin(angle) = opposite side / hypotenuse
* sin(45°) = southward component / 310 m
* southward component = sin(45°) * 310 m ≈ 219.2 m
3. Pythagorean Theorem: Now that we know the southward component, we can use the Pythagorean theorem to find the total distance (hypotenuse):
* hypotenuse² = southward component² + eastward component²
* hypotenuse² = (219.2 m)² + (219.2 m)² (since the eastward and southward components are equal in a 45-degree angle)
* hypotenuse² ≈ 96000 m²
* hypotenuse ≈ √96000 m² ≈ 309.8 m
Answer
The reindeer moves approximately 309.8 meters across the tundra.