1. A helicopter hovers 150 metres above the ground. The pilot observes a landing pad at an angle of depression of 28°. How far horizontally is the helicopter from the landing pad?

2. A 12-metre ladder leans against a wall. The foot of the ladder is 3.5 metres from the base of the wall. What angle does the ladder make with the ground?

3. From the top of a 45-metre tall lighthouse, a ship is spotted at an angle of depression of 15°. A second ship is spotted at an angle of depression of 22°. How far apart are the two ships?

4. A cable car travels up a mountain slope at an angle of 35° to the horizontal. If the cable car travels 800 metres along the cable, what is the vertical height gained?

5. A surveyor needs to find the height of a building. Standing 50 metres from the base, the angle of elevation to the top is 42°. Standing 80 metres from the base, the angle of elevation is 28°. Use both measurements to verify the building's height and explain any differences in your calculations.

6. An aeroplane takes off and climbs at a constant angle. After travelling 2.5 kilometres along its flight path, it has gained 450 metres in altitude.
a) What angle is the plane climbing at? _____________
b) How far horizontally has the plane travelled? _____________
c) If it continues at this angle for another 3 kilometres along the flight path, what will be its total altitude? _____________

7. Extension Challenge: A rectangular garden is 20m × 15m. A diagonal path is built from one corner to the opposite corner. A fountain is placed at the point where this diagonal intersects with a line drawn perpendicular from the third corner to the diagonal. Calculate the distance from each corner of the garden to the fountain.

8. Self-Assessment: Check the boxes that apply to your work today:

9. Reflection: Which type of trigonometry problem do you find most challenging and why?