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
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)
Radius or Radians.
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.
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
you have a triangle formed by the radius on 2 and the chord on the other. the angle in that triangle that is opposite the chord, find its measure in radians take that measure (in radians) and multiply it by the radius to get the arc length
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)
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.
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.
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.
Radius or Radians.
The arc length divided by the radius is the angle in radians. To convert radians to degrees, multiply by (180/pi).
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.
In order to find radians, you simply have to put Arc Length over Radius. Radius = 20 Arc Length = 45 45/20 = radians radians = 2.25
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
you have a triangle formed by the radius on 2 and the chord on the other. the angle in that triangle that is opposite the chord, find its measure in radians take that measure (in radians) and multiply it by the radius to get the arc length
When the angle is measured in radians arc_length = angle x radius. So, 20cm = angle x 12cm => angle = 20cm / 12cm ~= 1.67 radians
Equal to the length of the radius.