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A central angle of a circle of radius 30 cm intercepts an arc of 6 cm Express the central angle in radians and in degrees?
A central angle is measured by its intercepted arc.
Let's denote the length of the intercepted arc with s, and the length of the radius r. So,
s = 6 cm and r = 30 cm.
When a central angle intercepts an arc whose length measure equals the length measure of the radius of the circle, this central angle has a measure 1 radian.
To find the angle in our problem we use the following relationship:
measure of an angle in radians = (length of the intercepted arc)/(length of the radius)
measure of our angle = s/r = 6/30 = 1/5 radians.
Now, we need to convert this measure angle in radians to degrees.
Since pi radians = 180 degrees, then
1 radians = 180/pi degrees, so:
1/5 radians = (1/5)(180/pi) degrees = 36/pi degrees, or approximate to 11.5 degrees.
What else can I help you with?
What does a zero with a horizontal line through it mean?
It means a central angle measured in radians. ex. Convert 360 degrees radians. 180 degrees = pi radians so 360 degrees = pi radians/180 degrees = 360pi radians/180 = 2 pi radians
What is 2115 degrees in radians?
pi [radians] = 180 [degrees] 1 [degree] = pi/180 [radians] = 0.0174533 [radians] therefore, 2115 [degrees] = 2115 [degrees] * 0.0174533 [radians/degree] = 36.9 [radians]
Degrees to radians?
Degrees x 0.01745 = radians
Convert degrees to radians 47.6925 degrees to radians?
47.6925 deg = 83.24 radians.
What is 120 degrees to radians?
120 degrees = 2.0944 radians.
What does a zero with a horizontal line through it mean?
It means a central angle measured in radians. ex. Convert 360 degrees radians. 180 degrees = pi radians so 360 degrees = pi radians/180 degrees = 360pi radians/180 = 2 pi radians
What is the measure of the central angle of a circle with radius 5 m that intercepts a 2 m arc?
It is: 2/10pi times 360 = 23 degrees rounded Or, more simply, it is 2/5 = 0.4 radians.
What is the radian measure of the central angle of a circle of radius 18 feet that intercepts an arc of length 10 ft?
It is 10/18 = 0.55... radians.
What is 2115 degrees in radians?
pi [radians] = 180 [degrees] 1 [degree] = pi/180 [radians] = 0.0174533 [radians] therefore, 2115 [degrees] = 2115 [degrees] * 0.0174533 [radians/degree] = 36.9 [radians]
What is 35 degrees in radians?
To convert degrees to radians, you can use the formula: radians = degrees * (π/180). Therefore, 35 degrees is approximately 0.6109 radians.
Degrees to radians?
Degrees x 0.01745 = radians
What is the measure of the central angle of a circle with the arc length of 29.21 and the circumference of 40.44?
arc length/circumference = central angle/2*pi (radians) So, central angle = 2*pi*arc length/circumference = 4.54 radians. Or, since 2*pi radians = 360 degrees, central angle = 360*arc length/circumference = 260.0 degrees, approx.
Convert degrees to radians 47.6925 degrees to radians?
47.6925 deg = 83.24 radians.
What is 120 degrees to radians?
120 degrees = 2.0944 radians.
How many radians in 350 degrees?
There are 6.1 radians (rounded) in 350 degrees. (6.108652 radians).
Formula in changing radians to degree?
To go from radians to degrees, multiply by 180/pi To go from degrees to radians, multiply by pi/180
How do you draw a triangle with a right angle that's 4cm?
Angles are measured in degrees or in radians, but not in centimeters.Angles are measured in degrees or in radians, but not in centimeters.Angles are measured in degrees or in radians, but not in centimeters.Angles are measured in degrees or in radians, but not in centimeters.
