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  1. 1Sine of 7π/6
  2. 2Secant of 2π/3
  3. 3Cosine of 3π/4
  4. 4Degrees to radians
  5. 5Radians to degrees
  6. 6Arc length from radians
  7. 8Double angle from sinθ
  8. 10Solving 2sinx−1=0
  9. 12Solving tanx=√3
  10. 14Law of sines for a side
  11. 15Law of cosines, finding a side
  12. 17Area with two sides and angle
  13. 19Inverse sine and cosine angles
  14. 20Evaluating log expressions
  15. 21Logs: solving log equation
  16. 22Solving ln(2x+1)=3
  17. 24Solving exponential growth
  18. 25Solving a cubic by factoring
  19. 26Remainder theorem
  20. 28Asymptotes of a rational function
  21. 30Arithmetic sequence term and sum
  22. 31Geometric sequence, 8th term and sum
  23. 33Vector magnitude and dot product
  24. 35Resolving a force vector
  25. 36Multiplying complex numbers

17Area with two sides and angle

Two sides of a triangle are 8 cm and 11 cm, and the angle between them is 30°. Find the area.

The area is 22 cm², using Area = ½ab sin C with a = 8, b = 11, and the included angle 30°, since sin 30° = ½. As a sanity check, a 90° angle would give the larger area 44 cm², so 22 for the smaller 30° angle makes sense.

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