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To produce the required answer, the question should state, "How do you calculate the radius of a sector with an angle of 1.5 radians and an area of 15 sq cm ?
If an angle of 1.5 radians sweeps out an area of 15 sq cm then this is proportional to an angle of 2π radians sweeping out the area of the circle, namely πr2.
1.5/2Ï€ = 15/Ï€r2 : 1.5/2 = 15/r2 : r2 = (2 x 15)/1.5 = 30/1.5= 20
If r2 = 20 then r = √20 = √(4 x 5) = 2√5
What else can I help you with?
How do you calculate the length of an arc of a circle?
The length of the arc is equal to the radius times the angle (angle in radians). If the angle is in any other measure, convert to radians first. (radians = degrees * pi / 180)
What is rad in geometry?
Radius or Radians.
How can calculate roots radius of an angle?
To calculate the radius of a circle given an angle's roots, you can use trigonometric functions. If you have an angle in radians, the radius ( r ) can be calculated using the formula ( r = \frac{d}{2 \sin(\theta/2)} ), where ( d ) is the distance between the two points on the circle defined by that angle. For angles in degrees, convert them to radians first. This method is commonly applied in geometry and trigonometry.
The ratio of the arc length to the radius?
The arc_length is given by the angle measured in radians times the radius of the arc. To convert degrees to radians divide by 180° and multiply by π radians. eg 45° = 45° ÷ 180° × π radians = π/4 radians. eg 60° = 60° ÷ 180° × π radians = π/3 radians.
How do you solve the arc length given only the central angle?
To solve for the arc length when given only the central angle, you also need the radius of the circle. The formula for arc length ( L ) is given by ( L = r \theta ), where ( r ) is the radius and ( \theta ) is the central angle in radians. If the angle is provided in degrees, convert it to radians by using the formula ( \theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180} ). Once you have both the radius and the angle in radians, you can calculate the arc length.
How can one find the arc length using radians?
To find the arc length using radians, you can use the formula: Arc Length Radius x Angle in Radians. Simply multiply the radius of the circle by the angle in radians to calculate the arc length.
How do you calculate the length of an arc of a circle?
The length of the arc is equal to the radius times the angle (angle in radians). If the angle is in any other measure, convert to radians first. (radians = degrees * pi / 180)
How does one calculate arc length when given the radius and angle measure in degrees?
To find the arc length given the radius and angle measure in degrees, you must first convert the angle from degrees to radians, using the formula: Degrees = Radians X (pi/180). Then take the radians and the radius that you are given, and put them into the formula of Q = (a/r) where Q is the angle in radians, a is the arc length, and r is the radius. When you have this, simple multiply both sides by the radius to isolate the a. Once you do this, you have your answer.
What is rad in geometry?
Radius or Radians.
What two conditions must be met in order to convert angular displacement to linear displacement?
To convert angular displacement to linear displacement, you need to know the radius of the circle or rotation and the angle of rotation in radians. By multiplying the radius by the angle in radians, you can calculate the linear displacement.
How do you find the length of an arc in a circle?
You can measure it with a string. If you want to calculate it based on other measurements, you can multiply the radius times the angle, assuming the angle is in radians. If the angle is in degrees, convert it to radians first.
How can calculate roots radius of an angle?
To calculate the radius of a circle given an angle's roots, you can use trigonometric functions. If you have an angle in radians, the radius ( r ) can be calculated using the formula ( r = \frac{d}{2 \sin(\theta/2)} ), where ( d ) is the distance between the two points on the circle defined by that angle. For angles in degrees, convert them to radians first. This method is commonly applied in geometry and trigonometry.
How do you find the angle with the radius and the arc length?
The arc length divided by the radius is the angle in radians. To convert radians to degrees, multiply by (180/pi).
The ratio of the arc length to the radius?
The arc_length is given by the angle measured in radians times the radius of the arc. To convert degrees to radians divide by 180° and multiply by π radians. eg 45° = 45° ÷ 180° × π radians = π/4 radians. eg 60° = 60° ÷ 180° × π radians = π/3 radians.
How do you solve the arc length given only the central angle?
To solve for the arc length when given only the central angle, you also need the radius of the circle. The formula for arc length ( L ) is given by ( L = r \theta ), where ( r ) is the radius and ( \theta ) is the central angle in radians. If the angle is provided in degrees, convert it to radians by using the formula ( \theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180} ). Once you have both the radius and the angle in radians, you can calculate the arc length.
How do you convert feet to radians?
In order to convert feet to radians, you will need to follow this equation: multiply by π/180Ã?. In order to convert radians to degrees, use this equation: multiply by 180Ã?/π.
Can you use arc length to find radius?
Yes, as long as you know the angle of the arc (between the two radii at its ends at the centre of the arc): arc_length = radius x angle_of_arc_in_radians → radius = arc_length ÷ angle_of_arc_in_radians To convert between degrees and radians: radians = π x degrees ÷ 180° → degrees = 180° x radians ÷ π
