1) A jogger runs directly east for 5 km, then turns and goes northwest for 7 km. He then travels directly south for 5 km. How far is he from the starting point? (km)

Question

2) In what direction is he from the starting point(measured as an angle counterwise from the east axis, units are deg)? (Northwest is the direction lying exactly half way between north and west.)

Answer 1

1. Northwest = (90+180)/2 = 135 deg.

X = hor = 5km + 7cos135 = 0.05km.

Y = ver = -5km + 7sin135 = -0.05km.

d = sqrt((0.05)^2 + (0.05))^2 = 0.71km.
= distance from starting point.

2. tanAr = Y/X = -0.05 / 0.05 = -1,
Ar = -77.58 deg. = Reference angle.
A = 180 + (-77.58) = 102.4 deg. = Direction.