Below is a screenshot of my Calculus textbook, Stewart's Calculus: Early Transcendentals 8th edition. It's taken from the chapter on Vectors.
In Example 6, they ask to find the magnitude of the torque, which is the magnitude of the cross product of the force F and the position vector r:
$\tau = |\vec{F} x \vec{r}| = |\vec{F}||\vec{r}|sin(\theta)$
Where $\theta$ is the angle between the two vectors.
As I understand it, the angle between two vectors is measured if you start both vectors at the same tail, right? So in the diagram above, wouldn't the angle between the two vectors actually be 180-75 = 105 degrees? If so, why does my textbook use 75 degrees in its calculations? Is it because the sine of either of these angles will be the same, since both angles are above the x-axis in the 1st and 2nd quadrants?
Edit: or is the position vector in this case extending from the bolt to the end of the wrench? If that's the case, then I can see why it would be 75 degrees, since you would put tail to tail.