What is an angle of elevation?
It is the angle measured upward from the horizontal to an object above your eye level — for example, looking up to the top of a tower. An angle of depression is the matching downward angle to something below you.
// maths › Right-Angle Trigonometry
Angles of elevation & depression
Solve angle-of-elevation and angle-of-depression problems linking a height, a horizontal distance, and the viewing angle with tan θ = height ÷ distance, in degrees or radians, shown on a scene with an observer, an object, and the angle arc.
tan θ = height / distance
Angle unit
Frequently asked questions
Why are elevation and depression angles equal?
Between the same two points, the angle of elevation from the lower point equals the angle of depression from the higher point, because they are alternate angles between parallel horizontal lines.
Can you give a worked example?
Standing 50 m from a tower with an angle of elevation of 40°, the height is distance × tan θ = 50 × tan 40° ≈ 41.95 m above eye level. The same angle in radians is 40° ≈ 0.6981 rad; the Degrees/Radians toggle switches the input and the working.
Which ratio do these problems use?
Almost always tangent, because the height is the side opposite the angle and the horizontal distance is the side adjacent to it, and tangent links exactly those two sides.
Where is this used in real life?
Surveyors measure building and mountain heights, air-traffic controllers track aircraft, lifeguards and coastguards judge distances to boats, and forestry workers estimate tree heights.