For any standard English (US, not Whitworth) or metric vee thread the tool's angle should be 60 degrees as viewed from the top AND it should have a radius or flat at the tip that is determined by the pitch. There's a somewhat complicated drawing for both US and for metric threads to define that flat or radius, but you won't go wrong if you make it to remove about 1/10 to no more than 1/8 of the thread's (a sharp vee thread of the same pitch's) depth from the tool's tip.
A flat is easier to grind on a tool. I suspect that the real reason why the standard drawings allow a radius is because that is what happens as the tool wears so allowing it is one way of prolonging tool life between sharpenings.
From appearances, the tool in the photo seems to have a rather large radius, but there is no way to tell the scale of the drawing. Nor do you state the pitch of your desired thread so it could be OK or it could need resharpening.