Trigonometric Ratios and Solving Triangles MCQ Test 5

1. 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?

2. 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?

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

4. 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?

5. 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?

6. 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)?

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

8. 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?

9. 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?

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