Year 11 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.Match each angle to its tangent.
- 30°
- 45°
- 60°
- √3
- 1
- 1/√3
2.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?
3.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?
4.An upright pole casts a shadow. Put these angles of elevation of the Sun in order, shortest shadow first.
- 75°
- 30°
- 45°
- 60°
5.A tree is 20 m tall. From a point on level ground the angle of elevation of its top is 30°. Take √3 = 1.73. How far is that point from the base of the tree, in metres?
6.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?
7.The Sun is 45° above the horizon. How long a shadow does an upright pole 12 m tall cast on level ground, in metres?
8.A ladder 10 m long leans against a wall and makes an angle of 60° with the ground. How far is the bottom of the ladder from the wall, in metres?

Answer key — Year 11 Maths — Heights and distances