Question

A family vacationed at a beach 120 mi east and 30 mi south of their home. Find the distance and the direction from their home to the beach.

Answer 1

To get the distance, use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Assuming the point where the home lies is at the origin (0,0), thus the beach lies at (120, -30). Substituting,
d = sqrt((120 - 0)^2 + (-30 - 0)^2)
d = sqrt(14400 + 900)
d = sqrt(15300)
d = 123.69 mi

For the direction, we can just use trigonometry. Let X be the angle:
tan X = opposite/adjacent
tan X = -30/120
X = arctan -0.25
X = -14.04 degrees, or 14.04 degrees below the horizontal, or 14.04 degrees south of east

Therefore the beach is located 123.69 miles, 14.04 degrees south of east from home.

Hope this helps~ :3