a 4 cm long chord subtends a central angle of 60° . the radial segment of this circle is
The Answer is 4
100% sure answer:"4"
Yes, the correct answer is 4cm.
Using the same method as before:
We know that the chord length is 4cm and the central angle is 60 degrees.
Draw the chord and a radius from the center to one endpoint of the chord, which divides the central angle in half and creates a right triangle.
The hypotenuse of the right triangle is the radius of the circle (which we want to find), and the opposite side is half the length of the chord (or 2cm). The angle opposite the 2cm side is 30 degrees.
So, using the sine function: sin(30) = 2/r
Solving for r: r = 2/sin(30)
r = 4
Therefore, the radius of the circle is 4cm.
4cm
To find the length of the radial segment of the circle, we need to use the properties of a circle and trigonometry.
First, let's understand what a chord and a central angle are. A chord is a line segment connecting two points on a circle, while a central angle is an angle formed by two radii extending from the center of the circle to the endpoints of the chord.
In this case, the chord is 4 cm long and subtends a central angle of 60°. We need to find the length of the radial segment, which is the line segment connecting the center of the circle to one of the endpoints of the chord.
To solve this problem, we can use the properties of an equilateral triangle. An equilateral triangle has all three sides equal in length, and each angle measuring 60°.
We can consider the chord as the base of an equilateral triangle, and the line segment connecting the center of the circle to the midpoint of the chord as the height of the triangle. The length of the height will be equal to the length of the radial segment.
Since the chord is 4 cm long, the height of the equilateral triangle can be found using trigonometry. Let's say the length of the height (radial segment) is 'h' cm.
Using trigonometry, we know that the height (h) can be calculated using the formula:
h = (b/2) * tan(theta/2)
where 'b' is the length of the base (chord) and 'theta' is the central angle subtended by the chord.
In this case, b = 4 cm and theta = 60°.
Substituting the values into the formula:
h = (4/2) * tan(60°/2)
= 2 * tan(30°)
= 2 * (1 / √3)
= 2 / √3
= (√3 * 2) / 3
Therefore, the length of the radial segment (h) is approximately (√3 * 2) / 3 cm.