Answer:
Yes (you are 75 mi from epicenter). Travel at least 7.91 mi south
Step-by-step explanation:
See the attached image.
The epicenter is the point at the upper right of the drawing. You are 60 miles west (left) and 45 miles south (down) from the epicenter. A right triangle is formed--apply the Pythagorean Theorem, (leg)^2 + (leg)^2 = (hypotenuse)^2.
[tex]x^2=60^2+45^2\\\\x^2=3600+2025\\\\x^2=5625\\\\x=\sqrt{5625}=75[/tex] This is within 80 mi, so you feel the quake.
Now (see image2) you go y miles south. You want the distance between you and the epicenter to be at least 80 mi. You have another right triangle with legs 60 and y + 45 and hypotenuse 80.
[tex](y+45)^2+60^2=80^2\\\\(y+45)^2+3600=6400\\\\(y+45)^2=2800\\\\y+45=\sqrt{2800}\\\\y=\sqrt{2800}-45 \approx 7.91 \rm mi[/tex]
