Final answer:
To find the length of the minor arc cut off by one of the diagonals of the pentagon, we need to determine the central angle formed by the diagonal in relation to the center of the circle and use the formula for arc length.
Step-by-step explanation:
To find the length of the minor arc cut off by one of the diagonals of a regular pentagon inscribed in a circle with a radius of 10, we need to determine the central angle formed by the diagonal in relation to the center of the circle. Since the pentagon is regular, each interior angle is 108 degrees.
The corresponding central angle can be found by dividing the interior angle by 2, giving us 54 degrees.
To find the length of the minor arc, we use the formula: length of arc = (central angle / 360) * circumference.
Substituting the values, we have: length of arc = (54 / 360) * 2 π * 10.
Calculating this, we get a length of approximately 9.42 units for the minor arc cut off by one of the diagonals of the pentagon.