Question 1: A person is standing on the ground looking up at the top of a tower. The angle of elevation from their eye level to the top of the tower is 35°. If the person is 1.5 meters tall and stands 50 meters away from the tower, calculate the height of the tower.

Answer: 73.4 meters

Question 2: Construct a triangle on the grid to represent a scenario where the angle of depression from a lighthouse to a boat is 20°. The horizontal distance between the lighthouse and the boat is 150 meters. Draw and label the angles accordingly.

Answer: N/A (drawing task)

Question 3: A drone is flying at a height of 120 meters above ground level. From a point on the ground, the angle of elevation to the drone is 45°. How far horizontally is the drone from that point?

Answer: 120 meters

Question 4: A ship is at sea level and observes a lighthouse at an angle of depression of 10°. If the lighthouse is 200 meters tall, calculate the horizontal distance from the ship to the lighthouse.

Answer: 1123.2 meters

Question 5: In a 3D setting, a student stands 30 meters away from a building and observes its top at an angle of elevation of 40°. The student’s eye level is 1.2 meters. Calculate the approximate height of the building.

Answer: 37.7 meters

Question 6: A helicopter is hovering at a height of 250 meters. From a point on the ground, the angle of depression to the helicopter is 30°. Construct a diagram and find the horizontal distance from the point to the helicopter.

Answer: 433 meters

Question 7: A person is looking at a mountain from a distance of 2 km. The angle of depression to the base of the mountain is 5°, and to the peak is 20°. Assuming the height of the person’s eye level is 1.6 meters, estimate the height of the mountain.

Answer: 345 meters

Question 8: A tower is 80 meters tall. From a point 150 meters horizontally away, the angle of elevation to the top is 60°. Calculate the height of the observer’s eye level on the ground.

Answer: 44 meters

Question 9: Construct a right-angled triangle on the grid to represent a scenario where the angle of elevation is 45°, and the horizontal distance is 100 meters. Mark all relevant angles and sides.

Answer: N/A (drawing task)

Question 10: A satellite is at an altitude of 500 km in space. From a point on Earth, the angle of elevation to the satellite is 30°. If the radius of the Earth is approximately 6371 km, calculate the distance from the observer to the satellite.

Answer: Approx. 8,600 km

Question 11: Identify and correct the error in this student’s reasoning: 'The angle of depression to a ship is 10°, and the ship is 200 meters away. Therefore, the height of the lighthouse must be 2000 meters.'

Answer: The mistake is assuming height equals horizontal distance; actually, height = distance * tan(angle)