Struggling with WASSCE Maths? Stop guessing. Let’s fix the gap step by step.
Angle of Elevation and Depression: Meaning, Diagrams and the Difference
What the angle of elevation and the angle of depression mean, how to draw them correctly, and why WAEC examiners keep reporting this as a weakness.
📚 Part of the Trigonometry Clinic: every lesson on trigonometry, elevation, depression and bearings, in one place.
Quick answer: what is the difference between the angle of elevation and the angle of depression?
The angle of elevation is measured up from the horizontal to the line of sight, when you look at something above you. The angle of depression is measured down from the horizontal, when you look at something below you. When two points look at each other, the two angles are equal.
Elevation and depression questions are some of the most generous questions on the WASSCE Mathematics paper. The trigonometry is usually one line. Yet year after year, the Chief Examiners report that many candidates lose most of the marks before they ever reach that line, because the diagram is wrong.
This lesson fixes that one step. By the end you will know exactly where each angle goes, why the two angles are equal, and how to turn a word question into a correct sketch every time.
📋 What the WAEC Chief Examiner reported
- 2020: solving problems on angles of elevation and depression was named as a weakness.
- 2018: many candidates did not attempt the angle of elevation question, and most of those who did could not draw the diagram it needed.
- 2025, Question 9 (a mast and a pillar): poorly answered by most candidates. Many could not show the information in a diagram, so every follow-up part went wrong.
- 2025, Question 4 (a lighthouse and two boats): well answered by most candidates who drew the diagram correctly.
How to win these marks back
- Draw the horizontal at the observer before anything else.
- Measure elevation and depression from the horizontal, never from the vertical.
- Copy the angle of depression down to the object using alternate angles.
- Only then choose tan, sin or cos from the sides you know and the side you want.
Source: WAEC Chief Examiners’ Reports, WASSCE (SC) 2025, Ghana: Mathematics (Core); WAEC Chief Examiners’ Reports, Mathematics (Core), 2018 and 2020
What is an angle of elevation?
Stand on level ground and look up at the top of a tower. Your eyes started out looking straight ahead, along the horizontal. To see the top, you lift your line of sight. The angle you lifted through is the angle of elevation.
Three things are always in the picture: the observer (where the angle is), the horizontal through the observer, and the line of sight to the object.
What is an angle of depression?
Now stand at the top of a cliff and look down at a boat. Again you start by looking straight ahead along the horizontal, and this time you lower your line of sight. The angle you lowered through is the angle of depression.
Angle of elevation vs angle of depression: the difference
| Angle of elevation | Angle of depression | |
|---|---|---|
| You look | up at the object | down at the object |
| Measured from | the horizontal, upwards | the horizontal, downwards |
| Angle sits at | the observer (lower point) | the observer (higher point) |
| Typical words | “from the foot”, “from a point on the ground” | “from the top of”, “from a cliff”, “from an aircraft” |
Here is the fact that makes most of these questions easy. If someone at the top looks down at a boat, and someone in the boat looks up at the top, the two angles are equal. The two horizontals are parallel, and the line of sight cuts across both of them, so the angles are alternate angles.
This is why you are allowed to “move” an angle of depression down to the object and work inside the right-angled triangle on the ground.
How to draw an elevation or depression diagram
Notice that the ratio comes last. Most wrong answers in examiners’ reports start with a calculator and a guessed ratio, before there is a diagram to read it from.
Worked example 1: angle of elevation
Question. From a point P on level ground, 30 m from the foot of a tree, the angle of elevation of the top of the tree is 40°. Find the height of the tree, correct to one decimal place.
\tan 40^\circ=\dfrac{h}{30}h=30\tan 40^\circ=25.2\text{ m}Worked example 2: angle of depression
Question. From the top of a vertical cliff 80 m high, the angle of depression of a boat at sea is 25°. How far is the boat from the foot of the cliff?
\tan 25^\circ=\dfrac{80}{d}d=\dfrac{80}{\tan 25^\circ}=171.6\text{ m}Check that it makes sense: a small angle of depression means the boat is far away, so d should be much larger than 80 m. It is.
The four mistakes that cost the most marks
- Measuring from the vertical. The angle of depression is never the angle between the cliff face and the line of sight.
- No horizontal line. Without it you cannot see where the angle belongs.
- Putting the depression angle inside the triangle at the top. Inside the triangle, the angle at the top is 90° minus the angle of depression.
- Guessing the ratio. Label opposite, adjacent and hypotenuse from the angle first, then choose.
Angle of elevation and depression practice questions
- From a point on level ground 50 m from the foot of a building, the angle of elevation of the top is 32°. Find the height of the building, correct to one decimal place.
- From the top of a tower 60 m high, the angle of depression of a car on level ground is 38°. How far is the car from the foot of the tower?
- A kite string 90 m long is pulled tight and makes an angle of 55° with the level ground. How high is the kite above the ground?
Show the answers
1. h=50\tan 32^\circ = 31.2 m
2. d=\dfrac{60}{\tan 38^\circ} = 76.8 m
3. The string is the hypotenuse, so h=90\sin 55^\circ = 73.7 m
✏️ Try it yourself
From the top of a lighthouse 45 m high, the angle of depression of a canoe is 18°. Draw the diagram first, then find how far the canoe is from the foot of the lighthouse.
Tap to see the answer
Move the 18° down to the canoe. d=\dfrac{45}{\tan 18^\circ} = 138.5 m (1 d.p.).
Angle of elevation and depression: frequently asked questions
Is the angle of elevation equal to the angle of depression?
Yes, when the two points are looking at each other. The horizontals at the two points are parallel, so the angles are alternate angles and equal.
What is the formula for the angle of elevation?
There is no special formula. Draw the right-angled triangle and use \sin, \cos or \tan. When the height and the distance along the ground are involved, \tan\theta=\dfrac{\text{opposite}}{\text{adjacent}} is usually the one.
Why must I draw the diagram?
Because WAEC usually asks for it (“illustrate the information in a diagram”) and gives marks for it, and because every later part depends on it. The 2025 report shows that candidates who drew it correctly answered well, and those who did not lost the whole question.
Keep learning
- Bearings in Mathematics: Questions and Answers With Diagrams
- Word Problems in WASSCE Mathematics: Questions and Answers
- Why Do I Understand Maths in Class but Fail Tests?
📚 See every lesson in the Trigonometry Clinic
✏️ Practise trigonometry in the Practice Zone
Written by
Dickson Sarpong
NTC-certified SHS Mathematics teacher in Ghana with WAEC marking experience, and author of The Bridge Series textbooks. Every lesson here is built around the mistakes WAEC examiners keep reporting.
About DicksonStuck? Ask a question
Want the whole topic, step by step? My textbooks, The Bridge to Mathematics and The Bridge to Additional Mathematics for SHS, follow the new curriculum and rebuild the basics as you go.
Read a free chapter →
