Trigonometric Ratios and Solving Triangles MCQ Test 2

1. 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?

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

3. 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?

4. For an acute angle in a right-angled triangle, what is the relationship between the tangent and cotangent of that angle?

5. In a triangle XYZ, if angle X is 100 degrees and side x is 12 units, what is the length of side z using the Law of Sines?

6. If in a triangle ABC, angle A is 160 degrees and side a is 20 units, what is the length of side c using the Law of Sines?

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

8. In a triangle ABC, if angle B is 60 degrees and side b is 9 units, what is the length of side a using the Law of Sines?

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

10. In a right-angled triangle, if one acute angle is 50 degrees, what is the measure of the other acute angle?

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

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

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

14. 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?

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

16. 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?

17. 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?

18. If in a triangle ABC, angle A is 40 degrees and side b is 15 units, what is the length of side c using the Law of Sines?

19. In a triangle ABC, if angle C is 90 degrees and side a is 10 units, what is the length of side b?

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

21. For a triangle ABC with angle A = 90 degrees, if side b is 12 units and side c is 15 units, what is the length of side a?

22. 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)?

23. 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?

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

25. 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?

26. For an acute angle in a right-angled triangle, what is the relationship between the sine and cosine of that angle?

27. 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?

28. 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?

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

30. If in a right-angled triangle, the sine of the angle is 0.8, what is the measure of the angle (in degrees)?

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

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

33. If in a triangle ABC, angle B is 80 degrees and side b is 12 units, what is the length of side a using the Law of Sines?

34. In a triangle ABC, if angle A is 50 degrees and side a is 8 units long, what is the length of the side opposite angle B (side b) using the Law of Sines?

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

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

37. 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)?

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

39. 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?

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