Physic Vector manipulation

Let i and j be the unit vector along the +x and +y direction respectively.
Hence, the 3 vectors can be written as:
20i , 15j and 25sin(30)i + 25cos(30)j
Their vector sum = [20+25sin(30)]i + [15+25.cos(30)]j
= 32.5i + 36.65j
The resultant dispacement vector
=square-root[32.5^2+36.65^2] m = 49 m (2 significant figures)
and at a bearing of arc-tan(32.5/36.65) degrees = 42 degrees (i.e. N42E)

In the north-south direction,

Resultant vector = 15 + 25cos30* = 36.65 m N

In the east-west direction,

Resultant vector = 20 + 25sin30* = 32.5 m E

So, the magnitude of resultant vector

= sqrt[(36.65)2 + (32.5)2]

= 49.0 m

2009-10-11 21:51:07 補充：
tan@ = 32.5 / 36.65

@ = 41.6*

So, the resultant vector is 49.0 m in the direction N41.6*E