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
Exam 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°.
a)
Draw and label a diagram to show the top of the cliff, T, the foot of the cliff, F, the flag marker, M, and the boat, B, labelling all the angles and distances given above.
b)
Find the distance from the boat to the foot of the cliff.
c)
Find the value of .
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