The circle below has center V, and its radius is 3ft. Given that =m∠WVX140°, find the length of the minor arc WX.Give an exact answer in terms of π, and be sure to include the correct unit in your answer.
Question
The circle below has center V, and its radius is 3ft. Given that =m∠WVX140°, find the length of the minor arc WX.Give an exact answer in terms of π, and be sure to include the correct unit in your answer.
Solution
The problem seems to be missing some information or there might be a typo. However, if you're asking how to find the length of a minor arc given the central angle and the radius of the circle, here's how you do it:
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First, you need to know that the circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the radius is 3ft, so the total circumference of the circle is C = 2π(3ft) = 6πft.
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The length of an arc (either minor or major) is a fraction of the total circumference. The fraction is determined by the ratio of the central angle to 360° (since there are 360° in a circle).
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Given that the central angle is 140°, the fraction of the total circumference that the minor arc WX represents is 140°/360° = 7/18.
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Therefore, the length of the minor arc WX is (7/18) of the total circumference, which is (7/18)*6πft = 7π/3 ft.
So, the length of the minor arc WX is 7π/3 ft.
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