20.3 Angles of elevation and depression — Practise

Work independently. Estimate where useful, show your method, and check units. In the mixed questions, choose the method and give a reason.

1. A point is 10 m from a tower. The elevation angle is 45°. Find the height above eye level.
2. A building is 20 m high. The angle of elevation from a point is 30°. Find the horizontal distance.
3. A kite string is 50 m long and makes a 30° angle with the ground. Find its vertical height.
4. A hill rises 12 m over a horizontal distance of 16 m. Find the angle of elevation to 1 decimal place.
5. From a cliff top 30 m above sea level, the depression angle to a boat is 45°. Find the horizontal distance.
6. A tree casts a 6 m shadow when the sun elevation is 60°. Find its height.
7. A person observes a roof at 35° elevation from 18 m away. Find the rise to 1 decimal place.
8. A plane is 500 m above ground. Its depression angle to a runway point is 10°. Find horizontal distance to nearest metre.