Find the radius of a circle with a central angle of pi/7 and a length of the intercepted arc equal to 7.7 cm. Round your answer to the nearest tenth.

L=r*aplha

alpha in radians

L=7.7
alpha=pi/7

7.7=r*(pi/7) divide with (pi/7)
r=7.7/(pi/7)
r=(7.7*7)/pi
r=53.9/3.1415926535
r=17,1569cm
r=17.2cm

To find the radius of the circle, we can use the formula:

r = (s / θ)

Where r is the radius, s is the length of the intercepted arc, and θ is the central angle.

In this case, the length of the intercepted arc is 7.7 cm and the central angle is π/7.

Substituting these values into the formula, we get:

r = (7.7 cm) / (π/7)

To calculate this, we can convert the central angle from radians to degrees:

θ (in degrees) = (180° / π) * θ (in radians)
θ (in degrees) = (180° / π) * (π/7)

θ (in degrees) = 180° / 7

θ (in degrees) ≈ 25.714°

Now we can substitute the values back into the formula:

r = (7.7 cm) / (25.714°)

Calculating this, we get:

r ≈ 0.2995 cm

Rounding to the nearest tenth, the radius of the circle is approximately 0.3 cm.