An angle has a measure of 61 degrees plus 1.1 radians.
Determine the percentage of a circle's circumference cut off by this angle. _____% Determine the measure of this angle in radians. ______ radians
Determine the measure of this angle in degrees. _____ degrees
Determine the value of s, the arc length (measured in inches) cut off by this angle when centered in a circle with a radius of 2.8 inches. ______ inches
The measure of the angle is
61*(π/180)+1.1 redians
61+1.1*(180/π) degrees
now divide that by 2π or 360° to get the % of circle
arc length is s = rθ where θ is in radians.
Ok for the radians it's 2.16465084 radians and degrees is 124.02535746 degrees.
Well, isn't it amusing how angles can be measured in both degrees and radians? Let's get started!
To determine the percentage of a circle's circumference cut off by this angle, we need to find the measure of the angle in radians. The given angle is 61 degrees plus 1.1 radians. So, the angle in radians is 61° + 1.1 radians.
Now, let's calculate the measure of this angle in radians. Since 1 radian is equal to 180/π degrees, we can convert the 61 degrees to radians: 61° * (π/180) radians.
To determine the percentage of the circle's circumference cut off by this angle, we need to calculate the angle in radians and then divide it by 2π (the full circle in radians) and multiply by 100%. Let's do the math!
Angle in radians: 61° * (π/180) radians
Percentage of circle's circumference: (Angle in radians / 2π) * 100%
As for the measure of this angle in degrees, it's already given as 61 degrees.
Lastly, let's determine the arc length, s, cut off by this angle when centered in a circle with a radius of 2.8 inches. The formula for arc length, s, is s = r * θ, where r is the radius and θ is the angle in radians.
So, let's put on our clown noses and calculate away!
To determine the percentage of a circle's circumference cut off by an angle, you need to calculate the angle measure in radians and then convert it to a percentage.
1. To find the angle measure in radians, we add 61 degrees and 1.1 radians:
Angle in radians = 61 degrees + 1.1 radians
2. To convert the angle from degrees to radians, we use the conversion factor that 1 radian is equal to 180/π degrees:
Angle in radians = (61 degrees + 1.1 radians) × (π/180)
3. After calculating the angle in radians, we can convert it to a percentage of a circle's circumference. A full circle has 2π radians, which corresponds to 100% of the circle's circumference. Therefore, the percentage can be calculated as:
Percentage = (Angle in radians / 2π) × 100%
To find the measure of the angle in radians and degrees, we substitute the given values into the formulas.
To find the value of s, the arc length in inches, cut off by this angle when centered in a circle with a radius of 2.8 inches, we can use the formula for arc length:
Arc Length = r × θ
where r is the radius of the circle and θ is the angle in radians.
To calculate the values, substitute the given angle measure and the radius into the formula.