Question

Trent is running along a circular track that has a radius of 47 meters. Trent starts at the 3-o'clock position and travels in the CCW direction, stopping after 92 meters. Imagine an angle with a vertex at the center of the circular track that subtends the path Trent has traveled, The angle that Trent swept out along the arc has a measure of how many radians?

Answer 1

To find the angle δθ in radians that Trent swept along the arc, divide the arc length (92 meters) by the radius of the circle (47 meters) to get δθ ≈ 1.9574 radians.

Step-by-step explanation:

The angle θ that Trent swept out along the arc on the circular track can be found using the relationship between the arc length (θ), the radius of the circle (r), and the angle in radians. Since we know that the circumference of the circle is given by the formula 2πr and one complete revolution is equivalent to an angle of 2π radians, we can calculate the angle for any arc length by using the formula:

δθ = θ / r

Where:

• θ is the arc length in meters
• r is the radius in meters
• δθ is the angle in radians

In Trent's case, the radius (r) is given as 47 meters, and he has traveled an arc length (θ) of 92 meters. Applying these values to the formula, we get:

δθ = 92 / 47

After performing the division, we find that the angle δθ in radians is approximately:

δθ ≈ 1.9574 radians

We can use this angle to give us a better understanding of how far Trent has traveled in terms of angular distance around the track. The result is rounded to four decimal places for precision.