A chord subtends an angle of 68° at the centre of a circle of radius 200mm. Find the length of the chord.
if the chord length is 2x, then half the chord subtends half the angle:
x/200 = sin 34°
To find the length of the chord, we can use the following formula:
Length of the chord = 2 * radius * sin(angle/2)
Where:
- The radius is given as 200mm
- The angle is given as 68°
Plugging in these values, we can solve for the length of the chord:
Length of the chord = 2 * 200mm * sin(68°/2)
First, let's convert the angle from degrees to radians:
68° * (π/180) = 1.19 radians
Now, let's plug in the values:
Length of the chord = 2 * 200mm * sin(1.19/2)
Next, let's calculate the sine of half the angle:
sin(1.19/2) = 0.513
Now, let's plug this value back into the formula:
Length of the chord = 2 * 200mm * 0.513
Finally, let's calculate the length of the chord:
Length of the chord = 205.3mm
Therefore, the length of the chord is approximately 205.3mm.
To find the length of the chord, we can use the formula:
Length of Chord = 2 * Radius * Sin(Angle/2)
where Radius is the radius of the circle and Angle is the angle subtended by the chord at the center of the circle.
In this case, the radius is given as 200mm and the angle is given as 68°.
First, we need to convert the angle from degrees to radians since the trigonometric functions in the formula use radians.
Angle in radians = Angle in degrees * (π/180)
Let's calculate the angle in radians:
Angle in radians = 68° * (π/180)
Next, we can substitute the values into the formula:
Length of Chord = 2 * 200mm * Sin(68° * (π/180)/2)
Now, we can calculate the length of the chord using a calculator or by finding the value of Sin(34°) and substituting it back into the formula.
Length of Chord = 2 * 200mm * Sin(34°)
By evaluating the expression, we get:
Length of Chord ≈ 2 * 200mm * 0.559193
Length of Chord ≈ 223.677mm
Therefore, the length of the chord is approximately 223.677mm.