An angle of elevation is measured upwards from the observer’s horizontal; depression is measured downwards. For the same line of sight, these angles are equal when the two horizontals are parallel. Draw the horizontal reference before forming a triangle. Example In the diagram, the baseline is at eye level and h is the height above that level. An observer’s eye is 1.6 m above level ground and 20 m horizontally from a vertical building. The angle of elevation to its top is 35. Height above eye level is 20tan35, so building height is 20tan35 +1.6 15.6 m. The horizontal distance is adjacent to the elevation angle; the line of sight is the hypotenuse. Add eye height only when finding height above the same ground level.

An angle of elevation is measured upwards from the observer’s horizontal; depression is measured downwards. For the same line of sight, these angles are equal when the two horizontals are parallel. Draw the horizontal reference before forming a triangle.

In the diagram, the baseline is at eye level and \(h\) is the height above that level. An observer’s eye is 1.6 m above level ground and 20 m horizontally from a vertical building. The angle of elevation to its top is \(35^\circ\). Height above eye level is \(20\tan35^\circ\), so building height is \(20\tan35^\circ+1.6\approx15.6\text{ m}\).

The horizontal distance is adjacent to the elevation angle; the line of sight is the hypotenuse. Add eye height only when finding height above the same ground level.

Elevation, depression and heights

Elevation, depression and heights