Sine, cosine and tangent
Use the three trigonometric ratios to find a missing side.
Planned. This module is part of the plan and is not written yet.
Why it matters
Builders use trigonometry to cut roof rafters to the right length for a slope, and installers use it to tilt solar panels towards the sun.
Draft outline · in review- For
- Level 9–10 · JSS 3 (BECE) to SSS 1
- Inside
- 5 lessons and a test · about 90 minutes
- Topic
- Right-angled trigonometry · core, 2 of 4
Inside the module.
5 lessons in order, about 90 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: Naming the sides
Label the hypotenuse, opposite and adjacent sides from a given angle.
Explain15 min, from minute 0
Lesson 2: Ratios that stay the same
Measure similar triangles and find that opposite ÷ hypotenuse is fixed for each angle.
Investigate15 min, from minute 15
Lesson 3: Sine, cosine and tangent
Meet the three ratios and a way to remember them: SOH CAH TOA.
Explain15 min, from minute 30
Lesson 4: Finding sides
Choose the right ratio and rearrange it to find a missing side.
Worked example25 min, from minute 45
Lesson 5: Review
Mixed questions, with feedback on each.
Review20 min, from minute 70
End-of-module test
Label the sides of right-angled triangles from a given angle, and use sine, cosine or tangent to find missing sides.
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 90 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 roof rafter is 4 m long and makes an angle of 35° with the horizontal. How high does it rise? Give your answer 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
- Label the hypotenuse, opposite and adjacent sides from a given angle.
- Choose and use sine, cosine or tangent to find a missing side.
Unlocks
Level
Level 9–10 · JSS 3 (BECE) to SSS 1
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
2 of 4 · Core
Time
About 90 minutes
Alignments
- Aligned to WASSCEpartial · in reviewWASSCE Mathematics syllabus: trigonometric ratios
- Aligned to GCSEpartial · in reviewGCSE Mathematics: trigonometric ratios in right-angled triangles (descriptive ref)
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-04Multiplying and dividing togetherMaths · Primary 3 to Primary 4 (Level 3–4) · Planned Needs Division as sharing and grouping (required).
- 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 · the destination Needs Pythagoras' theorem (required), Unknowns on both sides (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.