Question 1: An engineer is inspecting the top of a tower. From a point 50 meters horizontally from the base of the tower, the angle of elevation to the top is 30°. Calculate the height of the tower.

Answer: Please calculate using tan(30°) = height / 50

Question 2: A crane operator looks up at an angle of depression of 45° to a load hanging from the crane. If the load is 20 meters below the operator, what is the horizontal distance from the crane to the load?

Answer: Use tan(45°) = horizontal distance / 20

Question 3: Construct a right triangle on the grid where the angle of elevation is 40° and the vertical height is 15 meters. Draw and label the triangle.

Answer: Use trig ratios to determine the hypotenuse and base.

Question 4: A building is 80 meters tall. From a point 100 meters away from its base, the angle of depression to the top of the building is 36°. Confirm the height of the building using the tangent ratio.

Answer: Calculate tan(36°) * 100 and add to the height if needed.

Question 5: In a construction project, an engineer observes that the angle of elevation to a beam's top from ground level is 25°. If the beam's height is 12 meters, find the distance from the observer to the base of the beam.

Answer: Apply tan(25°) = 12 / distance

Question 6: A drone is flying at a height of 150 meters. The angle of depression from the drone to a point on the ground is 20°. Calculate the horizontal distance between the drone and the point on the ground.

Answer: Use tan(20°) = 150 / distance

Question 7: A construction engineer observes that the angle of elevation to the top of a crane is 55°. When moving 30 meters closer horizontally, the angle of elevation increases to 65°. Calculate the height of the crane.

Answer: Use two tangent equations and solve for height.

Question 8: A lighthouse appears at an angle of depression of 10° from a ship 2 km away in the sea. Calculate the height of the lighthouse.

Answer: tan(10°) = height / 2000

Question 9: A surveying engineer measures the angle of elevation to a mountain peak from two different points on level ground. From point A, the angle is 20°, and from point B, 30°, with B being 500 meters closer to the mountain. Calculate the height of the mountain.

Answer: Set up two equations and solve for height.

Question 10: Identify and correct the mistake: An engineer calculates the height of a building using tan(θ) = opposite / adjacent, but mistakenly swaps the values, leading to an incorrect height. Explain the error and how to fix it.

Answer: Discuss swapping numerator and denominator and correct application.