Question 1: Calculate the angle of elevation from point A to the top of a building that is 50 meters tall, when observed from a point 80 meters horizontally away.

Answer: 30 degrees

Question 2: Determine the angle of depression from the top of a 60-meter-high lighthouse to a ship that is 150 meters away horizontally.

Answer: 22.6 degrees

Question 3: Construct a triangle on the grid where the angle of elevation from point P to the top of a tower is 45°, the horizontal distance is 100 meters. Draw and label the triangle accurately.

Answer: Height of tower = 100 meters

Question 4: A drone is flying 200 meters above the ground. From a point on the ground, the angle of elevation to the drone is 60°. Calculate the horizontal distance from the point to the drone's vertical projection.

Answer: 115.5 meters

Question 1: A person stands 150 meters away from a building. The angle of elevation to the top of the building is 35°. Calculate the height of the building. Explain your steps.

Answer: Height ≈ 91.3 meters

Question 2: A tower casts a shadow 80 meters long when the sun's elevation angle is 45°. Calculate the height of the tower. Show all working.

Answer: Height = 80√2 ≈ 113.1 meters

Question 3: An observer at the top of a 120-meter-high cliff looks down at an angle of depression of 20° to a boat in the sea. How far is the boat from the base of the cliff? Justify your answer.

Answer: Distance ≈ 344 meters

Question 1: A helicopter pilot observes an object on the ground with an angle of depression of 10°. If the helicopter is flying at an altitude of 300 meters, estimate the horizontal distance from the helicopter to the object.

Answer: Distance ≈ 1715 meters

Question 2: From the top of a 45-meter tall building, the angle of elevation to a satellite is 75°. Calculate the distance from the top of the building to the satellite. Assume the satellite is directly above a point on the ground aligned with the building.

Answer: Distance ≈ 172.2 meters

Question 1: A lighthouse is situated 250 meters from a ship at sea. The angle of depression from the top of the lighthouse (height 80 meters) to the ship is 18°. Find the height of the lighthouse if the ship is floating at the same level as the base of the lighthouse, and explain your solution.

Answer: Lighthouse height = 80 meters (already given), the problem tests understanding of angles of depression.

Question 2: Construct a 3D diagram where an observer looks at an object at an elevation angle of 60° from a point 150 meters away horizontally. Draw the scenario with accurate angles and label all parts.

Answer: Diagram for students to draw; height = 150 * tan(60°) ≈ 259.8 meters

Question 1: A student calculates the angle of elevation as 45° for a 100-meter-high building, but reports the height as 100 meters. What mistake might they have made? Correct the error.

Answer: Mistake: Used the angle as the height. Correct height: 100 meters.

Question 2: A student mistakenly swaps the roles of angles of elevation and depression in a problem. How does this affect the calculation? Provide a brief correction approach.

Answer: Swapping angles reverses the direction of calculation; must ensure correct angle corresponds to the correct scenario.