Question

Radius: 10 Arc Angle: Arc Length: 10/3 π find the Arc angle​

Answer 1

To find the arc angle, we can use the formula for arc length:

Arc length = (Arc angle/360) × 2πr

In this problem, we have the arc length and radius (r). We need to solve for the arc angle. The given information is:

Arc length = 10/3 π
Radius (r) = 10

Plug these values into the formula:

10/3 π = (Arc angle/360) × 2π × 10

To solve for the arc angle, we can follow these steps:

1. Divide both sides by 2π × 10 to isolate the Arc angle/360 term:
(10/3 π) / (2π × 10) = Arc angle/360

2. Simplify the left side of the equation:
(10/3) / 20 = Arc angle/360

3. Further simplify:
(10/3) / 20 = (10/60) = 1/6

So, 1/6 = Arc angle/360

4. Multiply both sides by 360 to solve for the arc angle:
Arc angle = 360 × (1/6)

5. Calculate the arc angle:
Arc angle = 60 degrees

The arc angle is 60 degrees.

Answer 2

The arc angle can be found by dividing the arc length by the radius. Given an arc length of 10/3 π and a radius of 10, the arc angle in radians is π/3.

Step-by-step explanation:

To find the arc angle when the radius of a circle is given, along with the arc length, you can use the relationship that the angle (in radians) is equal to the arc length divided by the radius. In this case, the given radius is 10 and the arc length is 10/3 π.

The formula to find the angle of rotation Δθ is:

Δθ = Arc Length / Radius

Now, plugging in the given values:

Δθ = (10/3 π) / 10

When simplified, it gives:

Δθ = π/3

So, the arc angle in radians is π/3.