Ratios and Graphs of Trigonometric Functions
Angle of depression
The angle measured downward from the horizontal to a line of sight.
| English | Angle of depression |
|---|---|
| Bahasa Melayu | Sudut tunduk |
| 中文 | 俯角 |
How it is used
From the top of a 50 m cliff, a boat is seen with an angle of depression of 25°. Its horizontal distance from the cliff base is 50 / tan 25° ≈ 50 / 0.466 = 107.2 m.
Where it shows up in SPM
Angle of depression appears in the Trigonometric Ratios chapter of Form 4. In Paper 2 it features in problems about looking down from cliffs, lighthouses or aircraft, usually solved with tangent after drawing the horizontal at the observer's level.
Don't confuse it with
Open the chapter: Ratios and Graphs of Trigonometric Functions →
Frequently asked questions
Why does the angle of depression equal the angle of elevation back?
The horizontal line at the top and the horizontal at the bottom are parallel. The line of sight is a transversal cutting both, so the angle of depression from above and the angle of elevation from below are alternate angles, which are equal.
A common mistake: is the angle measured from the vertical?
No. The angle of depression is always measured from the horizontal line at the observer, not from the vertical.
Drawing the horizontal first prevents the frequent error of using the complementary angle and getting the wrong ratio.