I drew a picture of your cone and labeled some points.
|PQ| = 58 mm and |QR| = 51 mm and the triangle PQR is a right triangle so be Pythagoras Theorem
|PR|2 = |PQ|2 + ||QR|2 = 582 + 512 = 3364 + 2601 = 5965
|PR| = √5965 = 77.23 mm.
Thus when you cone is rolled out flat it is a sector of a circle of radius 77.23 mm.
The length of the arc RS is the circumference of the circle at the base of your cone. This is a circle of radius 51 mm and the circumference of a circle of radius r is given by
circumference = 2 r = 2 51 = 320.44 mm.
All that remains is to determine the measure of the angle RPS. The relationship between the length of the arc of a sector of a circle, the radius of the circle and the angle at the center is
arc length = radius angle
where the angle is measured in radians. Thus
320.44 = 77.23 angle
angle = 320.44/77.23 = 4.15 radians.
There are radians in 180o and hence 4.15 radians is
4.15 180/ = 237.7o
Hence you need to draw a circle of radius 77.23 mm, cut out a sector with centre angle 360o - 237.7o = 122.3o . What remains is your template.