DSE 數學科：三角學

1. In a right-angled triangle, the side opposite θ is 5 and the hypotenuse is 13. What is sin θ?

2. Two sides of a triangle are 8 and 10, and the included angle is 30°. What is the area?

3. In triangle ABC, a = 7, A = 30° and B = 45°. Using the sine rule, b equals

4. In a triangle with sides 5, 5 and 6, what is the cosine of the angle opposite the side of length 6?

5. What is the period of y = sin(2x), with x in degrees?

6. The angle of elevation of the top of a tower, from a point 40 m from its foot on level ground, is 30°. What is the height of the tower?

7. Two sides and a non-included acute angle are given. Two different triangles exist when the side opposite the given angle is

8. Simplify (1 − cos^2 θ) / sin θ, where sin θ ≠ 0.

9. If a line makes an angle α with the normal to a plane, the angle between the line and the plane is

10. A triangle has sides 7, 8 and 9. The largest angle is opposite the side of length

11. Solve 2 sin x = 1 for 0° ≤ x ≤ 180°.

12. A vertical pole stands on horizontal ground. From a point 15 m from the foot, the angle of elevation of the top is 40°. The height of the pole is