the needle of the scale is 27 cm long. find the distance the tip of the needle travels when rotates 74 degree
what is 27cm*2PI*74/360
c = r * theta
74 deg = 74 * 2pi / 180 radians
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To find the distance the tip of the needle travels when it rotates by 74 degrees, we can use trigonometry.
First, let's draw a diagram to visualize the problem. We have a needle with a length of 27 cm, and it rotates an angle of 74 degrees.
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Let's call the distance the tip of the needle travels "d".
In this case, we want to find the arc length of the circular path traced by the tip of the needle, which is the distance "d".
To find the arc length, we can use the formula:
arc length = (angle/360 degrees) * (2 * π * radius)
where:
- angle is the angle of rotation in degrees
- radius is the length of the needle (in this case)
In our case, the angle is 74 degrees and the radius is 27 cm.
So we have:
arc length = (74/360) * (2 * π * 27)
Now we can compute it:
arc length = (74/360) * (2 * 3.14 * 27)
= (74/360) * (6.28 * 27)
= (74/360) * 169.56
≈ 34.987
Therefore, the distance the tip of the needle travels when it rotates by 74 degrees is approximately 34.987 cm.