Question

what is the resultant of displacement of 6 miles north and 9 miles east?

Answer 1

We may note that the displacements are perpendicular to each other, so we may use Pythagorean theorem to obtain the total displacement.

The total displacement is $S=\sqrt{l_1^2+l_2^2} =\sqrt{6^2+9^2}\approx 10.8$ miles. Next, we should determine the angle $\theta$ of the displacement with respect to the north.

$\cos\theta=\dfrac{6}{10.8} , \, \theta \approx 56^\circ.$

So now we know the total distance and the direction of the displacement.