You walk east 749 feet to get from your house to class. after class, you walk southwest 800 feet to meet your friends for lunch. when walking the 305 feet back home from lunch, what direction are you traveling?

We will assume that the road from house to class leads to the east. Than you go to the southwest. We will try to find the angle between the lines that lead from the house to class and from lunch back home.

By the cosine law:

800² = 749² + 305² - 2 · 749 · 305 · cos α

640 000 = 561 001 + 93 025 - 456 890 cos α

cos α = 0.03

α = cos (-1) (0.03) = 88.28°

So it is a little less than 90°.

Direction back home is North northwest (NNW).