AI generatedGeometry and measuresKey Stage 3

Angles of depression

Angles of depression.

  • Label the sides and angles before choosing a rule.
  • Sine rule: matching opposite pairs. Cosine rule: three sides or two sides and the included angle.
  • Use degree mode. Keep full calculator accuracy until the final rounding step.

Example 1

The horizontal distance is 15 m and the angle of depression from the top is 20°. Find to 1 decimal place.

Angle of depression15 m20°Diagram not to scale
The angle of depression equals the angle of elevation by alternate angles.Multiply both sides by the horizontal distance.Round only the final height.

Example 2

The horizontal distance is 16 m and the angle of depression from the top is 21°. Find to 1 decimal place.

Angle of depression16 m21°Diagram not to scale
The angle of depression equals the angle of elevation by alternate angles.Multiply both sides by the horizontal distance.Round only the final height.

Your turn

Question 1

The horizontal distance is 17 m and the angle of depression from the top is 22°. Find to 1 decimal place.

Angle of depression17 m22°Diagram not to scale
Check answer
The angle of depression equals the angle of elevation by alternate angles.Multiply both sides by the horizontal distance.Round only the final height.
Question 2

The horizontal distance is 18 m and the angle of depression from the top is 23°. Find to 1 decimal place.

Angle of depression18 m23°Diagram not to scale
Check answer
The angle of depression equals the angle of elevation by alternate angles.Multiply both sides by the horizontal distance.Round only the final height.
Question 3

The horizontal distance is 19 m and the angle of depression from the top is 24°. Find to 1 decimal place.

Angle of depression19 m24°Diagram not to scale
Check answer
The angle of depression equals the angle of elevation by alternate angles.Multiply both sides by the horizontal distance.Round only the final height.
Question 4

The horizontal distance is 20 m and the angle of depression from the top is 25°. Find to 1 decimal place.

Angle of depression20 m25°Diagram not to scale
Check answer
The angle of depression equals the angle of elevation by alternate angles.Multiply both sides by the horizontal distance.Round only the final height.
Question 5

The horizontal distance is 21 m and the angle of depression from the top is 26°. Find to 1 decimal place.

Angle of depression21 m26°Diagram not to scale
Check answer
The angle of depression equals the angle of elevation by alternate angles.Multiply both sides by the horizontal distance.Round only the final height.
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