Question

In a circle with radius 8, an angle intercepts an arc of length start fraction, 20, pi, divided by, 3, end fraction 3 20π ​ . find the angle in radians in simplest form.

Answer 1

The angle in radians that intercepts an arc of length 20π/3 in a circle with radius 8 is 5π/6 radians.

Step-by-step explanation:

To find the angle in radians, we use the relationship that the arc length (s) intercepted by an angle (θ) in a circle with radius (r) is given by s = rθ. Here, the radius (r) is 8 and the arc length is 20π/3. Setting up the equation for this problem, we get:

20π/3 = 8θ.

Now, we solve for θ:

θ = (20π/3) / 8 = 20π / 24 = 5π / 6.

Therefore, the angle in radians that intercepts an arc of length 20π/3 in a circle with radius 8 is 5π/6 radians.