91Ó°ÊÓ

The magnitude of the resultant vector is always in reverse order when two vectors are obtained along the two sides of a triangle.

The vector representation of vectors and by reversing the order is represented as

Fig: Vector representation

The magnitude of the resultant vector is

$R=\sqrt{A^2+B^2}$

Here$A$is the magnitude of the vector$A$(displacement towards west), and$B$is the magnitude of the vector$B$ (displacement towards north).

Substitute $18.0m$for $A$ and $25.0m$for $B$.

The direction of the compass is

$âˆ\dots ={\tan }^{-1}\left(\frac{A}{B}\right)$

Substitute role="math" localid="1668685940044" $18.0m$for $A$and $25.0m$for.$B$

$$\begin{gathered} âˆ\dots ={\tan }^{-1}\left(\frac{18.0m}{25.0m}\right) \\ =35.8° \end{gathered}$$

Hence, the distance from the starting point is $30.8m$and the compass direction of a line connecting starting point to the final position is$35.8°$ west of north.