7.9m and 4.3°
step-by-step explanation:
let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ
for 3.5 south, y = -3.5
for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30
for 15 west, x = -15
total x = 8.2 * cos 30 – 15 ≈ -7.9
total y = -3.5 + 8.2 * sin 30 = 0.6
magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5
the magnitude is approximately 7.9 m
tan θ = y/x = 0.6/-7.9
the angle is approximately 4.3Ëš north of west