Hola Mr. Catron! Jeremy Scheer and I, Beau Fredericks, have an answer for your Pythagorean theorem question. You moved to the south 1.5 degrees or 90 miles and to the east 5 degrees or 300 miles. The Pythagorean theorem says to square 90 and 300 and add the products. Next find the square root of that number to find your distance, which is 313.21 miles to the southeast.
Answer provide by Jeremy Scheer and Beau Fredericks, Billings West High School