Arc Length Calculation in Circle with Given Angle and Radius

23 Mar 2024

What is the length of arc FH in circle G with m∠FGH = 60 degrees and FG = 19 units?

Can you determine the arc length of FH in circle G based on the given angle and radius?

The length of arc FH in circle G with m∠FGH = 60 degrees and FG = 19 units can be calculated by following these steps:

First, we need to determine the measure of the central angle, which is m∠FGH = 60 degrees.

Next, we calculate the radius of the circle, as FG is given as 19 units, it is the radius of the circle.

Using the formula for arc length - Arc length = (central angle/360) * 2π * radius, we can now plug in the values.

Substitute the values: Arc length = (60/360) * 2π * 19

Simplify and solve the equation: Arc length ≈ 0.1667 * 2π * 19 ≈ 19.8 units.

Therefore, the length of arc FH in circle G with m∠FGH = 60 degrees and FG = 19 units is approximately 19.8 units, rounded to the nearest hundredth.