Finding angles
Use inverse sine, cosine and tangent to find a missing angle.
Planned. This module is part of the plan and is not written yet.
Why it matters
A ramp for a wheelchair must not be too steep; from its rise and its length along the ground, inverse trigonometry gives its angle.
Draft outline · in review- For
- Level 10 · SSS 1
- Inside
- 4 lessons and a test · about 75 minutes
- Topic
- Right-angled trigonometry · core, 2 of 4
Inside the module.
4 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: Working back from a ratio
If you know the ratio, how do you find the angle?
Explain15 min, from minute 0
Lesson 2: Inverse functions
Use sin⁻¹, cos⁻¹ and tan⁻¹ on a calculator, rounding sensibly.
Worked example20 min, from minute 15
Lesson 3: Which ratio?
Decide from the two known sides whether sine, cosine or tangent fits.
Practice20 min, from minute 35
Lesson 4: Review
Mixed questions, with feedback on each.
Review20 min, from minute 55
End-of-module test
Use inverse trigonometric functions to find angles, choosing the right ratio from the sides you know.
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 ramp rises 0.5 m over a horizontal distance of 6 m. Find the angle it makes with the ground, 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
- Use inverse trigonometric functions to find an angle.
- Decide which ratio to use from the sides you know.
Needs first
Unlocks
Suggested before
Level
Level 10 · 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 75 minutes
Alignments
- Aligned to WASSCEpartial · in reviewWASSCE Mathematics syllabus: trigonometric ratios
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-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 · the destination Needs Sine, cosine and tangent (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.