An arc of circle subtends an angle of 140¤ at the center.if the radius of the circle is 10cm, find the length of the chord to the nearest centimeter
The length of the chord:
C = 2 r sin ( θ / 2 )
In this case:
r = 10 cm
θ = 140°
C = 2 r sin ( 140° / 2 )
C = 2 • 10 • sin ( 70° )
C = 20 • 0.9396926207
C = 18.793852415
C = 19 cm to the nearest centimeter
To find the length of the chord, we can use the formula:
Chord length = 2 * radius * sin(angle/2)
Step 1: Convert the given angle from degrees (°) to radians (rad).
140° * π/180 = 2.443 rad
Step 2: Substitute the values into the formula:
Chord length = 2 * 10cm * sin(2.443/2)
Step 3: Calculate the sine of half the angle:
sin(2.443/2) ≈ 0.982
Step 4: Substitute the sine value back into the formula:
Chord length ≈ 2 * 10cm * 0.982
Step 5: Calculate the chord length:
Chord length ≈ 19.64cm
Therefore, the length of the chord, to the nearest centimeter, is approximately 20cm.
To find the length of the chord, we need to use the formula:
Length of chord = 2 * Radius * sin(angle/2)
Given:
Radius (r) = 10 cm
Angle (θ) = 140°
First, we need to convert the angle from degrees to radians since trigonometric functions use radians. To convert degrees to radians, we use the formula:
Radians = Degrees * π/180
So, for an angle of 140° in radians:
θ (in radians) = 140° * π/180 ≈ 2.443 radians
Now, substitute the values into the formula:
Length of chord = 2 * 10 cm * sin(2.443/2)
Calculating sin(2.443/2) gives us:
sin(2.443/2) ≈ 0.841
Substituting the values:
Length of chord = 2 * 10 cm * 0.841
Simplifying:
Length of chord ≈ 16.82 cm
Therefore, the length of the chord, to the nearest centimeter, is approximately 17 cm.