A circle of radius of 4 inches has an arc length of 5.8 inches. Find the measure of the central angle.

The radius of the circle is 4 inch and has an arc length of 5.8 inches . We know that if the central angle is 360° then the arc length is . Similarly when angle is theta ,

Now substitute respective values , from the given data ,

This is our required answer!

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

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