Final answer:
The girl scout hiked approximately 4.2130 miles East and 3.5354 miles South which rounds closest to option D: East: 3.5 miles, South: 5.5 miles. Therefore, the correct answer is option D. East: 3.5 miles, South: 5.5 miles
Step-by-step explanation:
When the girl scout hikes 5.5 miles at 40° South of East, we can use trigonometry to find out how far East and how far South she hiked. We can calculate the Eastward and Southward components of her hike by using the cosine and sine functions, respectively, because the hike can be represented as a vector with a magnitude of 5.5 miles and a direction of 40° South of East.
Using the cosine function for the Eastward component:
- East = 5.5 miles × cos(40°) ≈ 5.5 miles × 0.7660 ≈ 4.2130 miles
Using the sine function for the Southward component:
- South = 5.5 miles × sin(40°) ≈ 5.5 miles × 0.6428 ≈ 3.5354 miles
Therefore, the girl scout hiked approximately 4.2130 miles to the East and 3.5354 miles to the South. The correct answer would be closest to option D: East: 3.5 miles, South: 5.5 miles, if we are looking for answer choices that round to the nearest half mile.
Therefore, the correct answer is option D. East: 3.5 miles, South: 5.5 miles