A chord subtends an angle of 68 degrees at the center of a circle of radius 200mm.find the chord length.
Draw a diagram. If the chord has length 2x, then
x/200 = sin 34°
Why did the chord bring a protractor to the circle? Because it wanted to measure the angle of fun it was having! But seriously, let's calculate that chord length.
We can use the formula for calculating the length of a chord in a circle:
Chord Length = 2 * Radius * sin(Angle/2)
Substituting the given values:
Chord Length = 2 * 200mm * sin(68/2)
Calculating this:
Chord Length ≈ 2 * 200mm * sin(34)
Chord Length ≈ 2 * 200mm * 0.55919
Chord Length ≈ 223.68mm
So, the length of the chord is approximately 223.68mm.
Remember, it's all fun and games until someone brings a protractor to a circle!
To find the length of the chord, you can use the formula:
Chord length = 2 * radius * sin(angle/2)
Given that the radius of the circle is 200mm and the angle is 68 degrees, we can substitute these values into the formula:
Chord length = 2 * 200mm * sin(68/2)
First, we need to convert the angle from degrees to radians:
68 degrees * (π/180) = 1.19 radians
Now we can calculate the chord length:
Chord length = 2 * 200mm * sin(1.19/2)
Using the trigonometric identity sin(x/2) = √((1 - cos(x))/2), we can simplify the equation:
Chord length = 2 * 200mm * √((1 - cos(1.19))/2)
Now, we need to find the cosine of 1.19 radians:
cos(1.19) = 0.438
Substituting this value back into the formula:
Chord length = 2 * 200mm * √((1 - 0.438)/2)
Simplifying further:
Chord length = 2 * 200mm * √(0.562/2)
Chord length = 2 * 200mm * √(0.281)
Finally, calculate the chord length:
Chord length = 2 * 200mm * 0.529
Chord length = 211.6mm
Therefore, the length of the chord is approximately 211.6mm.
To find the length of the chord, you can use the formula:
Chord length = 2 * radius * sin(angle/2)
In this case, the radius is given as 200 mm, and the angle is given as 68 degrees.
Let's substitute these values into the formula and solve for the chord length:
Chord length = 2 * 200 mm * sin(68/2)
= 2 * 200 mm * sin(34)
≈ 2 * 200 mm * 0.559
≈ 223.6 mm
Therefore, the length of the chord is approximately 223.6 mm.