Grade 12 Math: Sine Ratio Worksheet

Grade 12 Math: Sine Ratio

Read each question carefully and show all your work. Round answers to two decimal places unless otherwise specified.

1. In a right-angled triangle, the sine of an angle is defined as the ratio of which two sides?

2. If sin(θ) = 0.5, what is the approximate value of θ in degrees?

3. For the right-angled triangle shown below, calculate the length of side 'x'.

4. A ladder leans against a wall, making an angle of 65° with the ground. If the ladder is 8 meters long, how high up the wall does it reach?

5. The maximum value of the sine function is   and the minimum value is  .

6. For an angle θ, sin(90° - θ) is equal to  (θ).

7. In a right-angled triangle, if the side opposite an angle is 5 units and the hypotenuse is 13 units, find the measure of the angle to the nearest degree.

8. An airplane takes off at an angle of elevation of 15°. If it has traveled 500 meters along its flight path, what is its current altitude?

9. If sin(A) = sin(B), then angle A must be equal to angle B.

10. The sine ratio can be greater than 1 for angles in a right-angled triangle.

11. A ship is sailing towards a lighthouse. The angle of elevation to the top of the lighthouse from the ship's deck is 10°. After sailing 500 meters closer, the angle of elevation increases to 18°. Calculate the height of the lighthouse.