Question

A plane flew 600 kilometers along a line 35° east of south. How far east of its starting point is it? How far south? Represent the given vectors.

Answer 1

We can find distance that the plane travels east from its starting point from the geometry:

$$cos\theta=\dfrac{d_x}{d},$$ $$d_x=dcos\theta=600\ km\cdot cos35^{\circ}=491.5\ km.$$

We can find distance that the plane travels south from its starting point from the geometry:

$$sin\theta=\dfrac{d_y}{d},$$ $$d_y=dsin\theta=600\ km\cdot sin35^{\circ}=344.14\ km.$$