Trigonometric Ratios and Solving Triangles MCQ Test 1

1. For an angle theta, if tan(theta) = 1.5, what is the corresponding cotangent of the angle?

2. In a right-angled triangle, if the length of one leg is 5 and the length of the hypotenuse is 13, what is the measure of the angle opposite the leg (in degrees)?

3. For a triangle ABC with angle A = 90 degrees, if side c is 17 units and side b is 8 units, what is the length of side a?

4. If the cotangent of an angle is 2, what is the corresponding acute angle (in degrees)?

5. In a right-angled triangle, if one acute angle is 45 degrees, what is the measure of the other acute angle?

6. What is the value of tan(75 degrees) in a right-angled triangle?

7. For an acute angle in a right-angled triangle, what is the relationship between the secant and cosecant of that angle?

8. In a right-angled triangle, if the hypotenuse is 15 units and one leg is 9 units, what is the length of the other leg?

9. In a right-angled triangle, if one acute angle is 65 degrees, what is the measure of the other acute angle?

10. What is the value of sin(60 degrees) in a right-angled triangle?

11. If in a triangle ABC, angle C is 90 degrees and side a is 20 units, what is the length of side b?

12. If in a triangle ABC, angle B is 75 degrees and side b is 20 units, what is the length of side c using the Law of Sines?

13. If angle A in a triangle is 60 degrees and angle B is 30 degrees, what is the measure of angle C?

14. In a right-angled triangle, if the tangent of an acute angle is 1.2, what is the measure of the angle (in degrees)?

15. If in a triangle ABC, angle B is 85 degrees and side b is 10 units, what is the length of side a using the Law of Sines?

16. If in a right-angled triangle, the cosine of the angle is 0.3, what is the measure of the angle (in degrees)?

17. What is the cosine of a 60-degree angle in a right-angled triangle?

18. In triangle PQR, if angle P is 85 degrees and side p is 15 units, what is the length of side q using the Law of Sines?

19. For an angle theta, if cosec(theta) = 1.5, what is the corresponding sine of the angle?

20. If in a right-angled triangle, the tangent of the angle is 0.75, what is the measure of the angle (in degrees)?

21. What is the value of cos(30 degrees) in a right-angled triangle?

22. In a right-angled triangle, if the length of one leg is 8 units and the length of the hypotenuse is 10 units, what is the measure of the other leg?

23. In a right-angled triangle, if the hypotenuse is 22 units and one leg is 15 units, what is the length of the other leg?

24. In a right-angled triangle, if the hypotenuse is 18 units and one leg is 12 units, what is the length of the other leg?

25. What is the value of cot(30 degrees)?

26. If in a triangle ABC, angle A is 140 degrees and side a is 15 units, what is the length of side c using the Law of Sines?

27. If in a triangle ABC, angle C is 95 degrees and side c is 18 units, what is the length of side a using the Law of Sines?

28. In a right-angled triangle, if the length of one leg is 5 units and the length of the hypotenuse is 13 units, what is the measure of the other acute angle (in degrees)?

29. If in a triangle ABC, angle A is 80 degrees and side a is 15 units, what is the length of side b using the Law of Sines?

30. If the tangent of an angle is 0.8, what is the corresponding acute angle (in degrees)?

31. In a right-angled triangle, if the hypotenuse is 10 units and one leg is 6 units, what is the length of the other leg?

32. If in a triangle ABC, angle A is 70 degrees and angle B is 50 degrees, what is the measure of angle C?

33. For an angle theta, if sec(theta) = 3, what is the corresponding cosine of the angle?

34. In a right-angled triangle, if one acute angle is 55 degrees, what is the measure of the other acute angle?

35. If in a triangle ABC, angle A is 75 degrees and side c is 12 units, what is the length of side b using the Law of Sines?

36. What is the value of cos(75 degrees) in a right-angled triangle?

37. If in a right-angled triangle, the cosine of the angle is 0.6, what is the sine of the angle?

38. If in a triangle ABC, angle B is 70 degrees and side b is 8 units, what is the length of side a using the Law of Sines?

39. For an angle theta, if cot(theta) = 1.8, what is the corresponding tangent of the angle?

40. If in a triangle ABC, angle A is 70 degrees and side c is 16 units, what is the length of side b using the Law of Sines?

41. For an angle theta, if cos(theta) = 0.707, what is sin(theta)?

42. If in a triangle ABC, angle C is 85 degrees and side c is 14 units, what is the length of side a using the Law of Sines?

43. For an angle theta, if sec(theta) = 2, what is the corresponding cosine of the angle?

44. In a right-angled triangle, if one acute angle is 70 degrees, what is the measure of the other acute angle?

45. In a right-angled triangle, if the length of one leg is 3 units and the length of the other leg is 4 units, what is the length of the hypotenuse?

46. For an angle theta, if cot(theta) = 1.5, what is the corresponding tangent of the angle?

47. In triangle PQR, if angle P is 75 degrees and side p is 12 units, what is the length of side q using the Law of Sines?

48. What is the value of cos(45 degrees) in a right-angled triangle?

49. If a triangle has angles A, B, and C, and side lengths a, b, and c, what trigonometric ratio is defined as the ratio of the length of the side opposite angle A to the length of the hypotenuse?

50. What is the value of tan(45 degrees)?