How one can calculate the effect of airplane angle deviation on the final position?

Question

Consider an airplane was moving along a flight path after x seconds it would pass a distance d1 K.M.. If the same airplane was moving with same speed at some angle from its original flight path, it would also pass the same distance d1 K.M..The question is how can one calculate the difference between the 2 paths?

Answer 1

Seems like simple 10th grade geometry. SOH-CAH-TOA?

Cosine, adjacent, hypotenuse

cosine of the angle = adjacent (red d1)/hypotenuse (blue d1)

Something like that, has been a long time

red d1 will not equal blue d1 unless the angle is 0.

Answer 2

Consider the angle to be $\alpha$ and the distance between them to be $x$. Then,

$\sin(\alpha) = \dfrac{x}{d_1}$

$\implies x= d_1\cdot\sin(\alpha)$