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How do you calculate the radius of a sector with an angle of 1.5 radians and 15cm. I have tried but I only ever get the answer of 10 or 2squareroot10 and the right answer is 2squareroot5?
GGirl113
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
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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.
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.
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
How do you find the measure of an arc knowing only the chord of arc and radius?
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
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.
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.
What is rad in geometry?
Radius or Radians.
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 many radians is a dog that has been tethered with a 20 foot lead if the length of the path is 45 feet?
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
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
How do you find the measure of an arc knowing only the chord of arc and radius?
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
A wire of length 20cm is bent so as form arc of circle of radius 12cm what is the angle subtended at the center in radians is?
When the angle is measured in radians arc_length = angle x radius. So, 20cm = angle x 12cm => angle = 20cm / 12cm ~= 1.67 radians
What is the length of an arc corresponding to an angle of one radians?
Equal to the length of the radius.
What is the general rule for establishing the correct length of the arc?
The length of an arc of a circle is the radius times the angle (in radians). So a full circle is an angle of 2*pi radians, and the circumference of a circle is 2*pi*radius. A half circle is pi*radius. Quarter circle is (pi/2)*radius, etc.
