The circle below has center V, and its radius is 9yd. Given that =m∠WVX160°, find the length of the major arc WYX.Give an exact answer in terms of π, and be sure to include the correct unit in your answer.WXV160°YLengthofmajorarcWYX:
Question
The circle below has center V, and its radius is 9yd. Given that =m∠WVX160°, find the length of the major arc WYX.Give an exact answer in terms of π, and be sure to include the correct unit in your answer.WXV160°YLengthofmajorarcWYX:
Solution
The problem seems to be missing some information or the information is not clearly stated. However, I'll provide a general solution based on the given information.
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First, we need to find the measure of the minor arc WX. Since ∠WVX is 160°, the measure of arc WX is also 160° because the measure of an arc formed by an angle at the center of a circle is equal to the measure of the angle.
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The measure of the major arc WYX is the difference between 360° (the total degrees in a circle) and the measure of the minor arc WX. So, the measure of the major arc WYX is 360° - 160° = 200°.
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The length of an arc is given by the formula (n/360) * 2πr, where n is the measure of the arc in degrees and r is the radius of the circle.
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Substituting the given values into the formula, we get (200/360) * 2π * 9 = 10π yd.
So, the length of the major arc WYX is 10π yards.
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