A chord subtends an angle of 68 degree at the centre of a circle of radius 200 mm.Find the length of the chord.
sin 34 = (x/2)/200
To find the length of the chord, we can use the formula:
Length of chord = 2 * radius * sin(angle / 2)
Given:
Radius = 200 mm
Angle = 68 degrees
Let's plug in the values into the formula:
Length of chord = 2 * 200 mm * sin(68 / 2)
We can simplify further:
Length of chord = 2 * 200 mm * sin(34)
Using a scientific calculator or a trigonometric table, we find that sin(34) is approximately 0.559193.
Plugging in the value for sin(34):
Length of chord = 2 * 200 mm * 0.559193
Calculating further:
Length of chord = 223.6772 mm
Therefore, the length of the chord is approximately 223.6772 mm.
To find the length of the chord, you can use the formula:
Length of Chord = 2 * Radius * sin(Angle/2)
In this case, the radius is given as 200 mm and the angle is given as 68 degrees.
First, we need to convert the angle from degrees to radians since the sin function takes input in radians.
Angle in radians = Angle in degrees * (π/180)
= 68 * (π/180)
Next, we can substitute the values into the formula:
Length of Chord = 2 * 200 * sin(68 * (π/180))
Now, we can calculate the length of the chord using a calculator or by using an approximate value of π (3.14):
Length of Chord ≈ 2 * 200 * sin(68 * (3.14/180))
After evaluating the expression, we find:
Length of Chord ≈ 400 * sin(1.19)
Finally, using a calculator, we can find the sine of 1.19 (in radians) and multiply it by 400:
Length of Chord ≈ 400 * 0.924
≈ 369.6 mm (rounded to one decimal place)
Therefore, the length of the chord is approximately 369.6 mm.