1. 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Right as Rain Ambiguous Anomaly Solving Sleuth Application Action Trigonometry Treat

2. Right as Rain - $100 The sides of an isosceles triangle are 5, 10, and 10 cm. Find the measures of its angles.

4. Right as Rain - $200 The angle of depression from the top of a tree to a point on the ground 100 meters from its base is 28 . How tall is the tree?

5. 53.17 m

6. Right as Rain - $300 If tan  = 7/6, evaluate cos .

8. Right as Rain - $400 A sonar operator on a cruiser detects a submarine at a distance of 500 m and an angle of depression of 37 . What is the depth of the submarine?

9. 300.91 m

10. Right as Rain - $500 The angle of elevation from point A to the top of a tower is 40 . The angle of elevation from point B to the top of the tower is 54 . If the distance from A to B is 10 feet, find the height of the tower.

11. 21.50 feet

12. How many solutions does the following triangle have? m  C = 55 , a = 11, c = 18 Ambiguous Anomaly - $100

13. One solution

14. Ambiguous Anomaly - $200 How many solutions does the following triangle have? m  B = 74 , a = 5, b = 4

15. No solutions

16. Ambiguous Anomaly - $300 How many solutions does the following triangle have? m  C = 52 , b = 8, c = 7

17. Two solutions

18. Ambiguous Anomaly - $400 If m  A = 23  and c = 17, find the length of a such that the triangle has no solutions.

19. 0 < a < 6.64

20. Ambiguous Anomaly - $500 If m  C = 34  and b = 46, find the length of c such that the triangle has two solutions.

21. 25.72 < c < 46

22. Solving Sleuth - $100 Solve  RST if m  R = 75 , m  S = 45 , and t = 3.

23. m  T = 60 , r = 3.35, and s = 2.45

24. Solving Sleuth - $200 Solve  ABC if a = 10, b = 11, and c = 12.

25. m  A = 51.3 , m  B = 59.2 , and m  C = 69.5 

26. Solving Sleuth - $300 Solve  PQR if m  P = 50 , q = 6, and r = 7.

27. m  Q = 55.6 , m  R = 74.4 , and p = 5.57

28. Solving Sleuth - $400 Solve  ABC if a = 17, b = 10, and c = 21.

29. m  A = 53.1 , m  B = 28.1 , and m  C = 98.8 

30. Solving Sleuth - $500 Solve  XYZ if m  X = 21.1 , x = 6, and y = 9.

31. m  Y = 32.7 , m  Z = 126.2 , and z = 13.45 and m  Y = 147.3 , m  Z = 11.6 , and z = 3.35

32. Application Action - $100 Find the area of a parallelogram that has sides measuring 23 and 15 meters and an included angle of 37 .

33. 207.63 square meters

34. Application Action - $200 A triangle has two sides measuring 36 and 10 units in length and an area of 24 square units. What is the measure of the included angle?

35. 7.7  or 172.3 

36. Application Action - $300 Find the area of a regular decagon inscribed in a circle with a radius of 11 inches.

37. 355.61 square inches

38. Application Action - $400 Find the lengths of the diagonals of a parallelogram that has sides measuring 11 and 18 meters and an included angle of 112 .

39. 17.22 and 24.36 units

40. Application Action - $500 Find the area of the figure shown. 15 115  10 8 100 

41. 141.78 square units

42. Trigonometry Treat - $100 How many solutions does the following triangle have? m  A = 63 , a = 3, b = 8

43. No solutions

44. Trigonometry Treat - $200 Solve  ABC if m  A = 100 , m  C = 30 , and c = 8.

45. m  B = 50 , a = 15.76, and b = 12.26

46. Trigonometry Treat - $300 617 9 118  Find the area of the figure shown.

47. 103.12 square units

48. Trigonometry Treat - $400 Two surveyors need to find the area of a triangular property. They start from a common point. Surveyor #1 walks 320 feet at a bearing of N64  E. Surveyor #2 walks for 270 feet at a bearing of S5  W. What is the distance between them?

49. 514.10 feet

50. Trigonometry Treat - $500 Find the length of the median from  A to in  ABC if a = 8, b = 4, and c = 6.

51. units