Angle of Elevation & Angle of Depression

When a person looks at something above his/her location, the angle between the line of sight and the horizontal is called the angle of elevation. In this case, the line of sight is "elevated" above the horizontal. Object Eye

When a person looks at something below his or her location, the angle between the line of sight and the horizontal is called the angle of depression. In this case, the line of sight is "depressed" below the horizontal. Eye Object

A stands at the window of a so that his are 12.6 m above the level ground in the vicinity of the An object is 58.5 m away from the on a line directly beneath the Find the angle of depression of the person's line of sight to the object on the ground.

Solutions  = angle of depression   12.15º  eye Line of sight 12.6m Ground level object 58.5m

Exercise Calculate the angle of elevation of the line of sight of a person whose eye is 1.7 m above the ground, and is looking at the top of a tree which is 27.5 m away on level ground and 18.6 m high.

Sketch

Solution   31.57º Angle of elevation of this person line of sight is 31.57º

Angle of depression Find the height of the man in the hot air balloon from the ground. = 50° h =100 tan 50° = 119.2m h 100m

FIND THE HEIGHT OF THE TOWER Exercise FIND THE HEIGHT OF THE TOWER Height of tower = 53 tan 80° = 300.6m 80º 53m

Exercise From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34º.  How far is the object from the base of the cliff?

Solution Let x m be the distance of the object from the base of the cliff.