Angles of elevation and depression
Heights, shadows and slopes: trigonometry in the real world, including the sun's angle.
Planned. This module is part of the plan and is not written yet.
Why it matters
You can find the height of a tall tree or a phone mast without climbing it: measure its shadow, or how far away you stand, and the angle up to the top.
Draft outline · in review- For
- Level 10–11 · SSS 1 to SSS 2
- Inside
- 5 lessons and a test · about 75 minutes
- Topic
- Right-angled trigonometry · extension, 3 of 4
Inside the module.
5 lessons in order, about 75 minutes in all, then a short test. Learners go at their own pace; the minutes are a guide, not a timetable.
Draft outline · in review
Lesson 1: Elevation and depression
Angles measured up from, or down from, the horizontal, and why the two are equal.
Explain15 min, from minute 0
Lesson 2: Drawing the diagram
Turn a description into a labelled right-angled triangle.
Worked example15 min, from minute 15
Lesson 3: Heights and distances
Solve problems about trees, buildings, hills and boats.
Practice20 min, from minute 30
Lesson 4: Shadows and the sun
Measure a pole's shadow and use the sun's angle to work out its height.
Investigate15 min, from minute 50
Lesson 5: Review
Mixed questions, with feedback on each.
Review10 min, from minute 65
End-of-module test
Draw diagrams for angle of elevation and depression problems, and solve them to find heights and distances.
Mastered at 85% or more. Retake it until you pass; nothing is lost, and each try gives feedback.
Already know it? A Challenge Test (planned) clears the whole module: 90% overall, no objective below 75%.
Last stageafter about 75 min
Practicalities
Draft outline · in reviewBuilt to run offline
Planned to run on the Lantern's own computer, with no internet needed.
Languages
Planned first in English; every module aims to reach all of the Lantern's languages.
Try a question.
One question from the module, as a learner would meet it. Have a go, then open the worked solution a step at a time.
Draft outline · in review
A tree casts a shadow 12 m long when the angle of elevation of the sun is 40°. How tall is the tree, to 1 decimal place?
Work it out on paper first, then show the answer and mark it yourself.
Particulars
Where it sits
What a learner can do after it
- Draw a diagram for a problem involving an angle of elevation or depression.
- Solve height and distance problems, such as the height of a tree from its shadow.
Needs first
Level
Level 10–11 · SSS 1 to SSS 2
Level mappings are approximate. A qualified teacher or lecturer in each country must check them before they appear in the app.
Difficulty for its level
3 of 4 · Extension
Time
About 75 minutes
Alignments
- Aligned to WASSCEpartial · in reviewWASSCE Mathematics syllabus: angles of elevation and depression
Alignment in review until a qualified teacher or lecturer checks it. No exam body, university or vendor endorses us; learners still sit the real exam.
Challenge Test
Planned: a Challenge Test to prove you know it and skip it. Pass at 90% overall, with no objective below 75%.
University courses it previews
Engineering, Surveying and Geoinformatics, Physics, Architecture
The route here.
Everything this module builds on, drawn as a route from its foundations. Solid lanes must be mastered first, or cleared by a Challenge Test; dashed lanes are suggestions that never lock anything.
- MA-ARI-OPS-01 Adding and subtracting, Level 1–3, Maths. Planned.
- MA-ARI-OPS-01Adding and subtractingMaths · Primary 1 to Primary 3 (Level 1–3) · Planned
- MA-ARI-OPS-02 Multiplication as equal groups, Level 2–3, Maths. Sample lesson in the demo.
- MA-ARI-OPS-02Multiplication as equal groupsMaths · Primary 2 to Primary 3 (Level 2–3) · Sample lesson in the demo Needs Adding and subtracting (required).Try the sample lesson: Multiplication as equal groups
- MA-ARI-OPS-03 Division as sharing and grouping, Level 3–4, Maths. Planned.
- MA-ARI-OPS-03Division as sharing and groupingMaths · Primary 3 to Primary 4 (Level 3–4) · Planned Needs Multiplication as equal groups (required).
- MA-ARI-OPS-04 Multiplying and dividing together, Level 3–4, Maths. Planned.
- MA-ARI-OPS-04Multiplying and dividing togetherMaths · Primary 3 to Primary 4 (Level 3–4) · Planned Needs Division as sharing and grouping (required).
- MA-ARI-ORD-01 Order of operations, Level 5–6, Maths. Planned.
- MA-ARI-ORD-01Order of operationsMaths · Primary 5 to Primary 6 (Level 5–6) · Planned Needs Multiplying and dividing together (required).
- MA-ALG-LIN-01What an equation meansMaths · Primary 5 to Primary 6 (Level 5–6) · Planned Needs Order of operations (required).
- MA-FDP-OPS-02Adding and subtracting with different denominatorsMaths · Primary 5 to Primary 6 (Level 5–6) · Planned · recommended
- MA-ALG-LIN-02One-step equationsMaths · Primary 6 (Level 6) · Planned Needs What an equation means (required).
- MA-ALG-LIN-03Two-step equationsMaths · Primary 6 to JSS 1 (Level 6–7) · Sample lesson in the demo Needs One-step equations (required), Adding and subtracting with different denominators (recommended).Try the sample lesson: Two-step equations
- MA-NUM-POW-01Squares, cubes and rootsMaths · Primary 6 to JSS 2 (Level 6–8) · Planned
- MA-ALG-LIN-04Unknowns on both sidesMaths · JSS 1 to JSS 2 (Level 7–8) · Planned Needs Two-step equations (required).
- MA-GEO-PYT-01Pythagoras' theoremMaths · JSS 2 to JSS 3 (BECE) (Level 8–9) · Planned Needs Squares, cubes and roots (required).
- MA-TRG-RAT-01Sine, cosine and tangentMaths · JSS 3 (BECE) to SSS 1 (Level 9–10) · Planned Needs Pythagoras' theorem (required), Unknowns on both sides (required).
- MA-TRG-RAT-02Finding anglesMaths · SSS 1 (Level 10) · Planned Needs Sine, cosine and tangent (required).
- MA-TRG-RAT-03Angles of elevation and depressionMaths · SSS 1 to SSS 2 (Level 10–11) · Planned · the destination Needs Finding angles (required).
Help light the room where this is learned.
Every route on this map starts in a classroom with 24 stations, a tutor that works offline and a facilitator upstairs. Four are planned and waiting for light.