Question

Instructions for finding a buried treasure include
the following: Go 585.3 paces at 156◦
,
turn to 215◦
and walk 282 paces, then travel
400 paces at 132◦
.
Find the magnitude of the resultant displacement
from the starting point.

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

585.3 paces at 156◦
cos 156 = -.914
sin 156 = .407
x distance = 585.3 *- .914 = - 525
y distance = 585.3 * .407 = + 238

282 at 215
cos 215 = -.819
sin 215 = -.574
x distance = 282 * -.819
y distance = 282 * -.574

400 at 132
cos 132 = - ....
sin 132 = + ...
x ....
y ....

Now add all the x distances X = .....
then Y = .....
figure out what quadrant by X and Y signs
tan (angle from x axis) = y/x

Answer 2

find the x and y components of the individual segments , then add
... the sine of the bearing is the x component , the cosine is the y component

(magnitude)^2 = x^2 + y^2

tan(bearing) = x / y

Answer 3

Scott, cos is x, they are using counterclockwise from east, not compass directions. Bothers me too (teach navigation).

Answer 4

oops ... got x and y reversed

sine is y ... cosine is x

tan(bearing) = y / x

Answer 5

and sorry, tan bearing = Y/X
we are used to navigating clockwise from north, but this is counterclockwise from east

Answer 6

But what about the second part? The direction?

Answer 7

As Scott and I both told you
to get the direction take the inverse tangent of Y/X

Answer 8

Be careful about the quadrant. If in quadrant 2 for example angle is between 90 and 180