A central angle θ in a circle of radius 8 m is subtended by an arc of length 9 m. Find the measure of θ in degrees. (Round your answer to one decimal place.)
θ = °
Find the measure of θ in radians. (Round your answer to two decimal places.)
θ = rad
since s = rθ,
8θ = 9
now multiply θ by 180/π to get the degrees.
To find the measure of the central angle θ in degrees, we can use the formula:
θ = (Arc length / Radius) × 180° / π
Given that the arc length is 9 m and the radius is 8 m, we can substitute these values into the formula:
θ = (9 / 8) × 180° / π
Simplifying this expression:
θ ≈ 102.86°
Therefore, the measure of θ in degrees is approximately 102.9°.
To find the measure of θ in radians, we can use the formula:
θ = Arc length / Radius
Given that the arc length is 9 m and the radius is 8 m, we can substitute these values into the formula:
θ = 9 / 8
Simplifying this expression:
θ ≈ 1.125 rad
Therefore, the measure of θ in radians is approximately 1.13 rad.
To find the measure of the central angle θ in degrees, we can use the formula:
θ = (arc length / radius) * (180 / π)
Given that the arc length is 9 m and the radius is 8 m, we can substitute these values into the formula:
θ = (9 / 8) * (180 / π)
Calculating this expression, we get:
θ ≈ 101.86°
Therefore, the measure of θ in degrees is approximately 101.9° (rounded to one decimal place).
To find the measure of θ in radians, we can use the formula:
θ = arc length / radius
Using the given values of the arc length (9 m) and the radius (8 m), we can substitute them into the formula:
θ = 9 / 8
Calculating this expression, we get:
θ ≈ 1.125 rad
Therefore, the measure of θ in radians is approximately 1.13 rad (rounded to two decimal places).
a. Circumference = 2pi*r = 6.28**8 = 50.3 m.
theta = (8/50.3)*360 = 57.3 deg.
b. 3.14/180 = x/57.3
X = --- rad.