Question 1: In a science experiment, a researcher points a sensor at a star located at a bearing of 045°. If the sensor is 30 meters from the starting point, what is the horizontal distance moved eastward?

Answer: 21.21

Question 2: Calculate the bearing from point A to point B if B is located 50 meters northeast of A.

Answer: 045

Question 3: A drone is flying at a bearing of 120° for 40 meters. What are its north and east components of movement?

Answer: {"eastComponent":"23.28","northComponent":"20"}

Question 4: Fluency & Practice: A scientist observes a satellite at a bearing of 270°. If the satellite is 60 meters away, what is its position relative to the observer?

Answer: 0, -60

Question 5: Problem Solving & Reasoning: During a field experiment, a robot points at a bearing of 150° from its starting point and travels 25 meters. How far north and east has it moved from the start?

Answer: {"east":"-14.76","north":"12.5"}

Question 6: A scientist needs to align a telescope at a bearing of 330° from the lab to observe a comet. If the telescope is 80 meters from the initial point, what are the east and north displacements?

Answer: {"east":"-52.23","north":"41.42"}

Question 7: Construct a triangle with sides representing movements of 30 meters at 60°, 40 meters at 150°, and 50 meters at 300° to practice bearing calculations.

Answer: Students will draw and verify accordingly.

Question 8: A satellite is located at a bearing of 200° from a ground station, 100 meters away. Calculate the satellite's position relative to the ground station in terms of east and north components.

Answer: {"east":"-86.60","north":"-34.20"}

Question 9: Challenge & Extension: A submarine navigates with a bearing of 135° for 70 meters. What is its displacement in north and east directions? Use precise calculations.

Answer: {"east":"-54.95","north":"34.85"}

Question 10: Error Analysis: A student calculates the bearing as 045° for a point northeast, but the actual bearing is 315°. Identify and explain the mistake.

Answer: The student misinterpreted northeast as a bearing of 045°; it should be 045° for northeast, while 315° points southwest.