A central angle subtends an arc of 35 cm. If the radius of the circle is 12 cm, what is the measure of the central angle?
arc= angleinRadian*radius
35/12= angle in Radians=2.91 radians=about 167degrees
To find the measure of the central angle, we need to use the formula:
Angle = (Arc Length / Radius)
In this case, the arc length is given as 35 cm, and the radius is 12 cm. Plugging in these values into the formula, we get:
Angle = (35 cm / 12 cm)
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 1 in this case:
Angle = 35 cm ÷ 12 cm
Calculating the division, we get:
Angle ≈ 2.917
Therefore, the measure of the central angle is approximately 2.917 radians.