where s=length of an arc, r=radius and Ф = angle in radians
The question asked us to find the angle
Given to us is; r =6m and s=52π and Фis what we are to find
From the formula s= rФ
Ф= s/r = 52πm/6m
Ф=52π/6
Ф=26π/3 radians
But the question states that the angle should be in degree, so we will change the above angle to degree, to do that we will simply multiply the angle by 180°/π
Thus;
Ф=26π/ 3 × 180°/π
(The π at the numerator will cancel that of the denominator, and 180° will be divided by 3 to give 60°, we will be left with just 26 and 60 at the numerator)
Ф = 26× 60°
Ф=1560°
Therefore, the central angle (in degree) subtended by an arc with length 52πmeters and radius 6 meters is 1560°
