I got 5 point Something, but I don’t think it’s correct. How can I write this in terms of pi?

Question

Given circle G, where IG = 6, and angle IGJ=48 degrees, determine the exact length of arc IJ.

Answer 1

Assuming G is the Central Angle and IG is the radius and J is another point of the circle:

An arclength is simply the length of a part of a circle. So to find the arclength, we take the circumference of a circle (2πr) and multiply it by the percentage of the circle represented by the central angle.

Remember percent can be calculated using is/of. So in your example angle IGJ is 48 degrees of a 360 degree cirlce. So the ratio, or percentage, that represents your specific arclength is (48/360).

Put it together and the arclength formula is (2πr)*(Θ/360)

Substitute your givens, r=6, Θ=48

2π(6)*(48/360) = 1.6π

Answer 2

The equation for arc length (S) is S = rθ however the angle θ MUST be in radian measure to use this equation.

There are π radians in 180° so we can set up a proportion:

π radians/180° = x radians/48°

Cross multiply and we have

48π = 180x

x = 48π/180 = 4π/15

Now, plug in the angle (4π/15) and the radius into the formula S = rθ

S = 6(4π/15) = 24π/15 = (8/5)π

Answer 3

The formula for arc length is L = degrees/360 * 2*π*r. This makes sense because an arc length is a portion of the circumference of a circle, and the circumference equation is C = 2*π*r. The portion of the circle covered is represented by the degrees/360.

Since I do not have a diagram, I am going to assume the diagram of the circle. G (the name of the circle) is also the center. I is a point on the circumference, so that makes 6 the radius because the definition of radius is the distance from the center to any point on the circumference. J is another point on the circumference. That makes the included angle 48 degrees.

Substitute 48 for degrees and 6 for the radius in the equation.

L = 48/360 * 2*π*6

Since you need the answer in terms of π, multiply everything but the π.

L = 8π / 5 or 1.6π

Rounded answer: L ≈ 5.03