Is there a hotkey to constrain the Tape Measure Tool to a tangent?
As you move in a tangent direction the line becomes magenta. You can hold down the shift key to keep that going.
The down arrow key might work too, but as that also locks inference to perpendicular, there is a chance it will lock to that instead of a tangent.
Be aware that the magenta tangent color indication in SketchUp means that the tool picks up one of the segments on either side of a vertex of a segmented curve, not the true tangent of a curve (as in true arc or circle). But then that magenta inference direction could be picked up from any edge in your model when hovering over that edge for a little while. Once you “put the edge direction into SketchUp’s memory” you will be able to get magenta and then lock it with [Shift] as @colin mentioned above.
I thought about that too. If you zoom into a circle or arc, and pick a midpoint of one of the segments, the tape measure line would be close to being a tangent, wouldn’t it?
For a midpoint you would be getting the right direction. But then it wouldn’t start at the right location. Midpoints aren’t located on the true circle. Endpoints are, though they don’t give the true tangent. Its edges on either side determine the magenta color indication. True tangent would be rather easy to construct though.