Angles-Of-Elevation-And-Depression Aqa Foundation

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Exam code:8300

Elevation & depression

What are angles of elevation and depression?

An angle of elevation or depression is the angle measured between the horizontal and the line of sight
- Looking up at an object creates an angle of elevation
- Looking down at an object creates an angle of depression
Right-angled trigonometry can be used to find
- an angle of elevation or depression
- or a missing distance
The tan ratio is often used in real-life scenarios
- You may know the height of an object and want to find the distance you are from it
- You may know the distance you are from an object and want to find its height

Diagram showing a person's face with a horizontal reference line at eye level. A diagonal line of sight pointing up towards a bird forms an angle of elevation and a line of sight pointing down towards a boat forms an angle of depression.

Examiner Tips and Tricks

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, T, stands 24 metres above the level of the sea.

The angle of depression from the top of the cliff to a boat at sea is 35°.

At a point $x$ metres vertically up from the foot the cliff is a flag marker, M.

The angle of elevation from the boat, B, to the flag marker is 18°.

(a) Draw a diagram of the situation. Label all the angles and distances given above.

Diagram showing a triangle BFT with an angle of elevation 35º marked between BT and the horizontal. The length Ft is equal to 24 m. A line is drawn from B to a point M on the line FT, such that angle FBM is equal to 18º. The height of MF is x m.

(b) Find the distance from the boat to the foot of the cliff.

Consider triangle TBF where F is the foot of the cliff
Angle TBF = 35º because of alternate angles

Use SOHCAHTOA to find the missing distance
We know the opposite (TF) and we want to find the adjacent (BF), so use $tan space theta equals straight O over straight A$

Triangle TBF with angle TBF = 35º, TF = 24 m. BT is marked as the hypotenuse, TF as the opposite and BF as the adjacent.

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Maths Gcse Aqa Foundation

Angles-Of-Elevation-And-Depression Aqa Foundation

Elevation & depression

What are angles of elevation and depression?

Examiner Tips and Tricks

Worked Example

Responses