Question 1: Calculate the bearing from point A to point B if the angle measured clockwise from North at point A is 045°. The distance between A and B is 150 meters.

Answer: 045

Question 2: A ship is located at point C. Its bearing from a lighthouse at point D is 120°. The lighthouse to ship distance is 200 meters. Calculate the bearing of the lighthouse from the ship.

Answer: 300

Question 3: Construct a triangle on the grid with sides measuring 80 meters, 120 meters, and 100 meters. Label the angles, assuming the side of 80 meters is between the 120 and 100 meters sides.

Answer: Angles approximately 40°, 60°, and 80°

Question 4: A vehicle travels from point P to point Q, which is 250 meters away. Its bearing from P to Q is 330°. What is the bearing from Q back to P?

Answer: 150

Question 5: Aerial survey shows a straight road with a bearing of 060° from point R to point S. If the distance between R and S is 300 meters, find the bearing from S back to R.

Answer: 240

Question 6: A boat is sailing at a bearing of 045° from the lighthouse. After 2 hours, it has traveled 50 km. Calculate its new bearing from the lighthouse assuming it maintains its course.

Answer: 045

Question 7: In a triangular plot, side AB measures 70 meters, side BC measures 100 meters, and side AC measures 80 meters. Calculate the measure of angle ABC using the cosine rule.

Answer: approximately 53°

Question 8: A pilot measures a bearing of 135° from his aircraft to a mountain. He then changes course to a bearing of 090°. If the mountain remains stationary 20 km from his starting point, what is the approximate distance from the aircraft to the mountain after the course change?

Answer: Approximately 25 km

Question 9: Identify and correct the mistake: A student calculates the bearing from point M to N as 180° when the correct bearing should be 360°. Explain what is wrong and provide the correct value.

Answer: The mistake is in the bearing notation; bearings are measured clockwise from North, so 360° is equivalent to 0°, not 180°.

Question 10: A ship at point X observes a lighthouse at a bearing of 075°. After moving 100 km due north, the ship observes the lighthouse at a bearing of 105°. Calculate the approximate distance between the ship's initial and final positions.

Answer: approximately 115 km

Question 11: Challenge: On the grid, construct a triangle with sides 150 meters, 200 meters, and 250 meters. Then, calculate the angles using the cosine rule and verify if the triangle is right-angled.

Answer: Angles approximately 53°, 90°, and 37°, with the triangle nearly right-angled at the 200m side.