Answer:
D) Joe need to walk 481 m in a direction 40.9° north of east
Explanation:
Given:
1. Walk 300 m north
2. Walk 400 m northwest
3. Walk 700 m east-southeast and the treasure is buried there
Taking north as positive y axis and east as positive x axis.
Resolving their positions into x and y vector components.
1. d1 = 300j
2. d2 = -400cos45i + 400sin45j
3 d3 = 700cos22.5i - 700sin22.5j
Resultant position.
d = d1+d2+d3
d = (-400cos45 + 700cos22.5)i + (300+400sin45-700sin22.5)j
d = (363.873)i + (314.964)j
D = √( (363.873)^2 + (314.964)^2)
D =481.25m ~= 481m
Angle = taninverse (314.964/363.873)
Angle = 40.9°
Since the x and y components are both positive, it implies that their position is north of east
Therefore, Joe need to walk 481 m in a direction 40.9° north of east
