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Math Problems on Arc Length, Sectors, Velocity, and Bearings

Solve math problems related to arc length, central angle, angular and linear velocity, bearings, and special triangles with detailed explanations. Improve your math skills with these practical exercises.

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Math Problems on Arc Length, Sectors, Velocity, and Bearings

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  1. Arc Length/ Sectors Angular & Linear Velocity DMS/ Nautical/ Bearing Special Triangles Rt Triangle Trig/Word 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500

  2. What is the exact length of an arc, with a central angle and radiusof 5 cm?

  3. A point 2 m from the center of a circle travels 4m. What is central angle in radians?

  4. A slice of 18” diameter pizza has an angle . What is the exact area of the slice?

  5. What is the measure of the angle (in degrees and rounded to the nearest hundredth), if the diameter is 5 inches and the arc length is 2 inches?

  6. What’s the exact angle in radians if the diameter is 3 inches and the arc length is ?

  7. A wheel is rotating at .The wheel has a radius of 30 cm. What is the speed in m/min?

  8. A 45 rpm record has a radius of 8.7cm. What is the linear velocity (to the nearest hundredth) of a fly on the edge of the record in cm/sec?

  9. A wheel has a 32cm diameter. The speed of a point on the rim is 11m/sec. What is the angular velocity of the point in radians per sec? (rounded to the nearest hundredth)

  10. 68.75rad/sec

  11. A water wheel has a 20’ radius. The wheel revolves 7 times per min. What is the speed of the wheel in miles/hour? (Round to the nearest hundredth)

  12. 10miles/hour

  13. A bucket is being raised in an old well at the rate of 3ft/sec. The radius of the drum being turned is 10inches. What is the angular speed of the handle in radians/second? (Round to the nearest hundredth)

  14. 3.60radians/second

  15. Convert to DMS.

  16. Convert to degrees.(Round to the nearest hundredth.)

  17. What is the bearing of NNW?

  18. 3500 statute miles is how many nautical miles? (Round to the nearest hundredth)

  19. 6300 nautical miles is how many statute miles? (Round to the nearest hundredth).

  20. 7249.75statute miles

  21. What is the ?

  22. 1/2

  23. What is the ?

  24. Undefined

  25. Given , what is the?

  26. 4/3

  27. If what is the ?

  28. If , what is ?

  29. What is the measure of <B to the nearest hundredth of a degree?

  30. 45.58degrees

  31. If , what is theta indegrees? (Round to the nearest hundredth).

  32. 39.52degrees

  33. Leave exact.

  34. A 6 foot person stands 120 feet from a tree with a line of sight to the top of the tree of 30 degrees. How tall is the tree? Round to the nearest hundredth.

  35. 75.28feet

  36. M<CAB=120 degrees A C B a What is the exact length of side a if the radius is 5?

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