Question

Assuming that the field of view is flat, what is the resultant vector (yellow line) of an observer pointing his telescope starting at the Andromeda galaxy, then moving 62 units 27

Answer 1

Assume the coordinates of the Andromeda galaxy are

$$\vec r_A=r_A\angle\theta_A,$$

we were given the coordinates to where the observer moves the telescope:

$$\vec r_t=r_t\angle\theta_t.$$

The resultant will be

$$r=\sqrt{(r_A\cos\theta_A+r_t\cos\theta_t)^2+(r_A\sin\theta_A+r_t\sin\theta_t)^2}=\\ =\sqrt{(r_A\cos\theta_A+55.2)^2+(r_A\sin\theta_A+28.1)^2},\\\space\\ \theta_r=\arctan\frac{r_A\sin\theta_A+r_t\sin\theta_t}{r_A\cos\theta_A+r_t\cos\theta_t}=\\\space\\ =\arctan\frac{r_A\sin\theta_A+28.1}{r_A\cos\theta_A+55.2}.$$