A 4cm long chord subtends a central angle of 60 degree what us the radial segment of the
circle
Well, it seems someone's been doing their math homework! But don't worry, I'm here to sprinkle a little humor on it.
Now, let's tackle this chord and central angle situation. The length of the chord is 4 cm, and it subtends an angle of 60 degrees.
To find the radial segment of the circle, we need to do a little circus act. Just kidding! We'll use a formula. The formula to calculate the radial segment of a circle is:
Radial segment = 2 × radius × sin (angle/2)
But wait, where's the radius? Oh, I hid it behind my ear! Okay, just kidding again. The radius is actually half the length of the chord. So, the radius is 4 cm divided by 2, which is 2 cm.
Now, let's substitute those values into the formula:
Radial segment = 2 × 2 cm × sin(60/2)
Now for the grand finale, let's calculate this. Drumroll, please...
Radial segment = 2 × 2 cm × sin(30)
Mathematicians know that sin(30) equals 0.5. So, let's wrap this up:
Radial segment = 2 × 2 cm × 0.5
Radial segment = 4 cm
Ta-da! The radial segment of the circle is 4 cm. And the crowd goes wild!
To find the radial segment of the circle, you can use the formula:
Radial segment = (r * θ) / 360
Where:
- Radial segment is the length of the radial segment of the circle
- r is the radius of the circle
- θ is the central angle in degrees
In this case, the central angle is 60 degrees and the length of the chord is 4 cm. We need to find the radial segment.
Since we don't have the radius directly given, we need to first find the radius using the chord length and central angle.
We can use the formula:
Chord length = 2 * r * sin(θ/2)
Where:
- Chord length is the length of the chord
- r is the radius of the circle
- θ is the central angle in radians
In this case, the chord length is 4 cm and the central angle is 60 degrees.
First, convert the central angle to radians:
θ (in radians) = θ (in degrees) * π / 180
θ (in radians) = 60 * π / 180
θ (in radians) = π / 3
Now, we can substitute the values into the chord length formula:
4 = 2 * r * sin(π / 3)
Simplifying further:
2 * r * sin(π / 3) = 4
sin(π / 3) = (√3) / 2 (approx. 0.866)
2 * r * (√3 / 2) = 4
r * √3 = 2
r = 2 / √3
Now that we have the radius (r), we can substitute it into the formula for the radial segment:
Radial segment = (r * θ) / 360
Radial segment = ((2 / √3) * π / 3) / 360
Simplifying further:
Radial segment = π / (3√3 * 360)
Radial segment ≈ 0.00621 cm
To find the radial segment of the circle, we need to calculate the radius of the circle first.
We know that a chord divides a circle into two segments. The radial segment is the part of the circle that lies between the chord and the center of the circle.
In this case, we are given the length of the chord, which is 4 cm, and the central angle, which is 60 degrees.
To find the radius, we can use the formula:
r = (c / 2) / sin(A / 2)
where r is the radius, c is the length of the chord, and A is the central angle.
Substituting the given values into the formula, we have:
r = (4 / 2) / sin(60 / 2)
r = 2 / sin(30)
r = 2 / (1/2)
r = 4
Therefore, the radius of the circle is 4 cm.
The radial segment of the circle is the part of the circle enclosed by the chord and the radius. Since the length of the chord is 4 cm, and the radius is also 4 cm, the radial segment of the circle is a sector with a central angle of 60 degrees and a radius of 4 cm.
Draw a radius through the center of the chord, and another to the end of the chord. Now you have a 30-60-90 triangle with the short leg = 2.
The radius of the circle is easily seen to be 4.