Elevation & Depression
What are the angles of elevation and depression?
- If a person looks at an object that is not on the same horizontal line as their eye-level they will be looking at either an angle of elevation or depression
- If a person looks up at an object their line of sight will be at an angle of elevation with the horizontal
- If a person looks down at an object their line of sight will be at an angle of depression with the horizontal
- Angles of elevation and depression are measured from the horizontal
- Right-angled trigonometry can be used to find an angle of elevation or depression or a missing distance
- Tan is often used in real-life scenarios with angles of elevation and depression
- For example if we know the distance we are standing from a tree and the angle of elevation of the top of the tree we can use Tan to find its height
- Or if we are looking at a boat at to sea and we know our height above sea level and the angle of depression we can find how far away the boat is
Examiner Tip
- It may be useful to draw more than one diagram if the triangles that you are interested in overlap one another
Worked example
A cliff is perpendicular to the sea and the top of the cliff stands 24 m above the level of the sea. The angle of depression from the cliff to a boat at sea is 35°. At a point m up the cliff is a flag marker and the angle of elevation from the boat to the flag marker is 18°.