Trigonometric Ratios and Solving Triangles MCQ Test 3

1. 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?

2. In a triangle ABC, if angle A is 120 degrees and side a is 14 units, what is the length of side b using the Law of Sines?

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

4. 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?

5. 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?

6. In a right-angled triangle, if one acute angle is 60 degrees, what is the measure of the other acute angle?

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

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

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

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

11. In triangle XYZ, if angle Y is 45 degrees and side x is 10 units, what is the length of side z using the Law of Sines?

12. 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?

13. If the sine of an angle is 0.6, what is the corresponding acute angle (in degrees)?

14. 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?

15. 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?

16. What is the sine of a 30-degree angle in a right-angled triangle?

17. If in a triangle ABC, angle B is 85 degrees and side b is 18 units, what is the length of side a using the Law of Sines?

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

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

20. 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?

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

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

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

24. In a right-angled triangle, if the length of one leg is 10 units and the length of the other leg is 24 units, what is the length of the hypotenuse?

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

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

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

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

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

30. 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?