Answer:
225 degrees
Step-by-step explanation:
Given the following data;
- Radius, r = 5.6 cm
- Length of arc = 22 cm
To find the angle in degrees subtended by an arc;
Mathematically, the length of the arc of a circle is given by the formula;
S = rA
Where;
- S is the length of the arc.
- A is the angle measured in radians.
Substituting the values into the formula, we have;
22 = 5.6 * A
[tex] A = \frac {22}{5.6} [/tex]
A = 3.9286 radians.
Next, we would convert the value of the angle in radians to degrees;
Conversion:
[tex] 1 \; radian = \frac {180}{\pi} \; degrees [/tex]
[tex] 3.9286 \; radians = X \; degrees [/tex]
Cross-multiplying, we have;
[tex] X = \frac {180}{\frac {22}{7}} * 3.9286 [/tex]
[tex] X = \frac {180 * 7}{22} * 3.9286 [/tex]
[tex] X = \frac {1260}{22} * 3.9286 [/tex]
[tex] X = 57.2727 * 3.9286 [/tex]
X = 225.0015 ≈ 225 degrees
