# A man walks 3 km due east and then 5 km northeast, how do you find his distance and bearing from his original position?

Mar 2, 2017

$7.43$ km ${28.4}^{\circ}$ North of East (approx.)

#### Explanation:

Using the Law of Cosines
$\textcolor{w h i t e}{\text{XXX}} c = \sqrt{{a}^{2} + {b}^{2} - 2 \cos \left(\angle C\right)}$
evaluated using a calculator
$\textcolor{w h i t e}{\text{XXX}} c \approx 7.4305 \ldots$

Using the Law of Sines
$\textcolor{w h i t e}{\text{XXX}} \sin \left(\angle B\right) = \frac{5}{c} \times \sin \left({135}^{\circ}\right)$
evaluated using a calculator
$\textcolor{w h i t e}{\text{XXX}} \sin \left(\angle B\right) \approx 0.4758 \ldots$
and
$\textcolor{w h i t e}{\text{XXX}} \angle B = \arcsin \left(0.4758 \ldots\right) \approx {28.412}^{\circ}$