Elevation and Depression

## Elevation and Depression

Elevation is the value, in degrees, that an object is above the observer. Create a triangle using the distance from the observer to the object, the height of the object above the ground, and the horizontal distance from the observer to the object.

Depression is the value in degrees that a value is below the observer. Establish a triangle in the same way as for an elevation.

## Example 1

An aircraft is flying above a building, which is known to be 5000m away. The elevation of the aircraft is 40º. How high is the aircraft above the building, to the nearest metre? Ignore the height of the building and the height of the observer.

The height is opposite the angle of elevation. The angle and adjacent side are known.

Use TOA from SOH CAH TOA

 TOA tan x = frac(text(opposite))(text(adjacent)) substitute tan (40) = frac(h)(5000) 0.839 x 5000 = h 4195.498 = h nearest metre 4195 = h

 TOA tan x = frac(text(opposite))(text(adjacent)) substitute tan (1) = frac(20)(x) x = frac(20)(tan (1)) x = frac(20)(0.0175) x = 1142.86 nearest m x = 1143