To find the length of the major arc, we first need to determine the measure of the central angle corresponding to the angle formed by the two tangents.
When two tangents intersect outside a circle, the angle formed is equal to half the difference of the intercepted arcs. In this case, the intercepted arc is the major arc.
Let's call the intercepted arc "x" inches. Therefore, the other arc intercepted by the tangents is (360 - x), as the sum of the intercepted arcs is equal to the total circumference of the circle, which is 360 degrees.
Since the formed angle is 105 degrees, it is equal to half the difference of the intercepted arcs:
105 = (1/2) * (x - (360 - x))
Now, we can solve this equation to find the value of x:
105 = (1/2) * (2x - 360)
210 = 2x - 360
2x = 570
x = 285
Thus, the major arc is 285 inches long.