Angles of Elevation and Depression

Key idea

Angles measured up or down from the horizontal.

In depth

The angle of elevation is measured upwards from the horizontal to a line of sight; depression is measured downwards. They are equal for the same sight line by alternate angles. Draw a right triangle with the horizontal as a side.

Worked example

From 50 m away a tower’s top has elevation 40°: height = 50 tan 40° ≈ 42 m.

Real-world uses

• Measuring the height of a lighthouse from a boat
• Estimating the depth of a well or a cliff

Common mistake

Measuring the angle from the vertical instead of the horizontal.

How to learn this

1. Read the key idea and say it in your own words.
2. Work through the worked example, then try a similar problem.
3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

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Related intermediate topics in Trigonometry

• Radians – Angle measured by arc length on a unit circle; 2π rad = 360°.
• Converting Degrees and Radians – Multiply by π/180 or 180/π.
• Sine Ratio – Opposite over hypotenuse.
• Cosine Ratio – Adjacent over hypotenuse.
• Tangent Ratio – Opposite over adjacent.
• Reciprocal Trig Functions – Cosecant, secant and cotangent.