the needle of the scale in bulk food section of a supermarket is 25 cm long. find the distance when the needle rotates 50 degrees
X = hor = 25cos50 = 16.1cm = distance.
To find the distance when the needle rotates 50 degrees, we need to calculate the circumference of the circle that the needle travels.
The circumference of a circle can be calculated using the formula:
C = 2πr
where C is the circumference and r is the radius of the circle.
Given that the needle's length is 25 cm, we can consider it as the radius of the circle.
So, the circumference of the circle is:
C = 2π(25) = 50π cm
Since the needle rotates 50 degrees, we need to find the arc length that corresponds to that angle.
The formula for the arc length is:
L = (θ/360) × C
where L is the arc length, θ is the angle in degrees, and C is the circumference of the circle.
Plugging in the values, we have:
L = (50/360) × (50π)
L = (5/36) × (50π)
L = (250/36)π
Approximating π to 3.14, we can calculate the arc length:
L ≈ (250/36) × 3.14 ≈ 21.81 cm
Therefore, the distance when the needle rotates 50 degrees is approximately 21.81 cm.
To find the distance when the needle rotates 50 degrees, we can use the concept of arc length.
The formula for arc length is given by:
Arc Length = Radius * θ
In this case, the needle of the scale can be thought of as the radius of a circle, and the angle it rotates (50 degrees) is denoted by θ.
Given that the needle of the scale is 25 cm long (which is equivalent to the radius), we can substitute these values into the formula:
Arc Length = 25 cm * 50 degrees
However, the formula for arc length is typically in radians, not degrees. So, we need to convert the angle from degrees to radians.
Conversion from degrees to radians can be done using the following formula:
θ (radians) = θ (degrees) * π / 180
Substituting the value of 50 degrees into the formula:
θ (radians) = 50 * π / 180
Now, we substitute this value into the arc length formula:
Arc Length = 25 cm * (50 * π / 180)
To calculate the value, we also need to know the approximate value of π, which is approximately 3.14159.
Arc Length = 25 cm * (50 * 3.14159 / 180)
Simplifying this equation, we get:
Arc Length = 25 cm * (0.872665)
Calculating the result:
Arc Length ≈ 21.82 cm
So, the distance when the needle rotates 50 degrees is approximately 21.82 cm.