Instructions for finding a buried treasure include the following: Go 745.6 paces at 298◦, turn to 204◦ and walk 178 paces, then travel 490 paces at 55◦

Question

Find the magnitude of the resultant displacement from the starting point. Answer in Units of paces.
(Part 2)
What is the direction of the resultant displacement? Use counterclockwise from due east as the positive angular direction, between the limits of −180◦ and +180◦. Answer in units of ◦

Answer 1

D = 745.6[298o] + 178[204o] + 490[55o]

X=745.6*cos298 + 178*cos204 + 490*cos55=
468.5 Paces.

Y=745.6*sin298 + 178*sin204 + 490*sin55=
-329.3 Paces.

Tan A = Y/X = -329.3/468.5 = -70291
A = -35.1o = 324.9o CCW = Direction.

Displacement=X/Cos A = 468.5/Cos 324.9 = 573 Paces.