Year 10 Maths — Heights and distances

Use angles of elevation and depression with the standard angles to find a height or a distance you cannot measure directly.

Name: ________________________

1.A ladder 10 m long leans against a wall and makes an angle of 60° with the ground. Take √3 = 1.73. How far up the wall does it reach, in metres?
2.From a window you look down at a car, and from the car someone looks up at the window. How do the angle of depression and the angle of elevation compare?
- a) They add up to 90°
- b) The angle of elevation is larger
- c) They are equal
- d) The angle of depression is larger
3.From the top of a cliff, the angle of depression of a boat is 30°. As the boat sails straight towards the base of the cliff, what happens to the angle of depression?
- a) It increases
- b) It stays the same
- c) It becomes an angle of elevation
- d) It decreases
4.A pole stands upright on level ground. From a point 10 m from its base, the angle of elevation of the top of the pole is 45°. How tall is the pole, in metres?
5.The angle of elevation of the top of a tower from a point on level ground is 60°, and the point is 45 m from the base of the tower. Take √3 = 1.73. How tall is the tower, in metres?
6.An upright pole casts a shadow. Put these angles of elevation of the Sun in order, shortest shadow first.
- 45°
- 75°
- 30°
- 60°
7.From the top of a cliff 40 m high, the angle of depression of a boat at sea is 45°. How far is the boat from the base of the cliff, in metres?
8.Someone at the top of a cliff is looking down at a boat. Tap the angle of depression.
Write the number of the part.

Answer key — Year 10 Maths — Heights and distances