The angular diameter of an object is the size of the object expressed as an angular measurement when it is viewed from a particular spot.

If an object is at a distance D from the point it is being viewed from and the diameter of the object as a length is L, the angular diameter A is given by the formula:

`A = 2*tan^-1(L/(2D))`

From the Earth, the Sun's angular diameter is 0.5. Let the distance of the sun from the Earth be represented by D. The diameter of the Sun as a length is:

`L = 2*D*tan(0.5/2) = 2*D*tan 0.25`

Now, Mercury is closer to the Sun and its distance from the Sun is equal to 0.387*D. The angular diameter of the Sun from Mercury is:

`2*tan^-1((2*D*tan 0.25)/(2*0.387*D))`

= `2*tan^-1((tan 0.25)/0.387)`

= 1.2919 degrees

As Pluto is at a distance equal to 39.53*D, the angular diameter of the Sun from Pluto is:

`2*tan^-1((2*D*tan 0.25)/(2*39.53*D))`

= `2*tan^-1((tan 0.25)/(39.53))`

= 0.1264 degrees

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