Multiple Choice

1. A ship sails from port A on a bearing of 045°. What is the bearing of port A from the ship?

   135°

   315°

   045°

   225°

2. A lighthouse is located at N30°E from a boat. What is the bearing of the boat from the lighthouse?

   S30°W

   N30°W

   S30°E

   E30°S

3. In triangle ABC, angle A = 40°, angle B = 60°, and side a = 10 cm. Which expression calculates the length of side b?

   10 sin(60°)/sin(40°)

   10 sin(40°)/sin(60°)

   10 sin(80°)/sin(40°)

   10 sin(40°)/sin(80°)

4. In triangle PQR, p = 8 cm, q = 12 cm, and angle P = 30°. Which expression calculates angle Q?

   sin⁻¹(12 sin(30°))

   sin⁻¹(12 sin(30°)/8)

   sin⁻¹(8 sin(30°)/12)

   sin⁻¹(8 sin(12°)/30)

5. In triangle XYZ, x = 5 cm, y = 7 cm, and angle Z = 60°. Which expression calculates the length of side z?

   sqrt(5² + 7² - 2 * 5 * 7 * cos(60°))

   sqrt(5² + 7² + 2 * 5 * 7 * cos(60°))

   sqrt(5² - 7² - 2 * 5 * 7 * cos(60°))

   (5² + 7² - 2 * 5 * 7 * cos(60°))²

6. In triangle MNO, m = 6 cm, n = 8 cm, and o = 10 cm. Which expression calculates angle O?

   cos⁻¹((6² + 8² + 10²)/(2 * 6 * 8))

   cos⁻¹((6² + 8² - 10²)/(2 * 6 * 8))

   cos⁻¹((8² + 10² - 6²)/(2 * 8 * 10))

   cos⁻¹((6² + 10² - 8²)/(2 * 6 * 10))

7. Find the area of a triangle with two sides measuring 8 cm and 10 cm, and the included angle is 45°.

   1/2 * (8 + 10) * sin(45°) cm²

   1/2 * 8 * 10 * sin(45°) cm²

   1/2 * 8 * 10 / sin(45°) cm²

   8 * 10 * sin(45°) cm²

8. A triangle has sides of length 7 cm, 8 cm, and 9 cm. What is its semi-perimeter?

   12.5 cm

   24 cm

   14 cm

   12 cm

9. Using Heron's formula, find the area of a triangle with sides 6 cm, 8 cm, and 10 cm.

   24 cm²

   48 cm²

   30 cm²

   12 cm²

10. Which rule would you use to find side 'c' in triangle ABC if you are given sides 'a' and 'b' and angle 'C'?

    Area Rule

    Sine Rule

    Cosine Rule

    Heron's Rule

11. Which rule would you use to find angle 'A' in triangle ABC if you are given all three sides 'a', 'b', and 'c'?

    Pythagorean Theorem

    Sine Rule

    Cosine Rule

    Area Rule

12. A boat travels 5 km on a bearing of 090° from point P to point Q. Then it travels 5 km on a bearing of 000° from point Q to point R. What is the straight-line distance from P to R?

    7.07 km (approx)

    10 km

    6.5 km

    5 km

13. In triangle ABC, angle A = 30°, angle B = 70°, and side c = 12 cm. Which of the following expressions correctly calculates the area of the triangle?

    1/2 * 12 * (12 sin(70°)/sin(30°)) * sin(80°)

    1/2 * 12 * (12 sin(80°)/sin(70°)) * sin(30°)

    1/2 * 12 * (12 sin(70°)/sin(80°)) * sin(30°)

    1/2 * 12 * (12 sin(30°)/sin(70°)) * sin(80°)

14. A helicopter flies 100 km on a bearing of 090° from A to B. It then flies 100 km on a bearing of 180° from B to C. What is the bearing of C from A?

    135°

    090°

    045°

    225°

15. A triangle has sides 7 cm, 9 cm, and 12 cm. Which expression calculates the largest angle in the triangle?

    cos⁻¹((7² + 12² - 9²)/(2 * 7 * 12))

    cos⁻¹((9² + 12² - 7²)/(2 * 9 * 12))

    sin⁻¹((12 sin(9°))/7)

    cos⁻¹((7² + 9² - 12²)/(2 * 7 * 9))

16. When using the Sine Rule to find an angle A, if sin A = 0.5, what are the two possible values for angle A between 0° and 180°?

    30° and 330°

    30° and 150°

    60° and 120°

    30° and 210°

17. A triangular garden has sides 15m, 20m, and 25m. What is its area?

    125 m²

    150 m²

    100 m²

    200 m²

18. A plane flies from airport X on a bearing of 050° for 200 km to airport Y. From airport Y, it flies on a bearing of 140° for 150 km to airport Z. What is the angle XYZ?

    100°

    90°

    80°

    130°

19. A triangular plot of land has sides 20m, 21m, and 29m. Calculate its area.

    200 m²

    290 m²

    180 m²

    210 m²

20. In a triangle, if you are given two angles and one side (AAS or ASA), which rule is most appropriate to find another side?

    Sine Rule

    Heron's Rule

    Cosine Rule

    Pythagorean Theorem