Topic 3: Trigonometry

Three 60-minute lesson plans on non-right-angled triangle trigonometry (sine rule, cosine rule, area of a triangle), pitched at DP AA (SL/HL), MYP Grade 10, and IGCSE Grade 10.

A. DP Mathematics: Analysis & Approaches — SL/HL, Year 1

Caveat: content below is drawn from the pre-publication draft syllabus (first assessment 2029, Topic C: Geometry, subtopic C2). Verify against the final published guide once released.

Anchor concept: Sine rule, cosine rule, and area of a triangle ((\frac{1}{2}ab\sin C)), applied to bearings and angles of elevation/depression (syllabus ref. C2). Taught in Year 1, following Functions per SOW_DP1_AAHL.

Prior knowledge assumed: Right-triangle trig ratios and Pythagoras (MYP5/IGCSE); basic bearings notation.

Learning objectives

Command terms used

Calculate / Find (sides, angles, areas); Show that (verifying a given result using the rules); Determine (which rule applies, and whether the ambiguous case arises).

Assessment focus (2029 draft AOs)

Problem specification — deciding which rule (sine, cosine, or area formula) fits a given triangle configuration; Computation — accurate multi-step calculation, often combined with bearings or 3D contexts.

ATL / skills focus

Thinking (selecting the correct rule from the information given — a genuine decision-making skill, not just formula recall); self-management (working through multi-step problems systematically, labelling diagrams clearly).

Starter (≈10 min)

Present a triangle with two sides and a non-included angle known (SSA case) and a triangle with two sides and the included angle known (SAS case). Ask: “Can you solve either of these using right-triangle trig alone? Why not?” — motivates the need for new rules.

Main teaching sequence (≈35 min)

  1. Introduce the sine rule (\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}); solve the SSA triangle from the starter, briefly flagging the ambiguous case (two possible triangles) without full derivation.
  2. Introduce the cosine rule (a^2=b^2+c^2-2bc\cos A) (and rearranged form for finding an angle); solve the SAS triangle from the starter.
  3. Introduce the area formula (\frac{1}{2}ab\sin C); apply it to both worked triangles as a check/extension.
  4. Multi-step application: a bearings problem requiring students to first sketch the triangle from worded bearings information, then choose and apply the correct rule(s).
  5. HL-only extension (last ~10 min): state (without full proof) (\sin(A+B)=\sin A\cos B+\cos A\sin B) and use it to find an exact value (e.g. (\sin 75°)) — flagged explicitly as a preview of the full identities lesson to come. SL students instead complete an extended bearings/elevation practice set.

Formative assessment / check for understanding

Before students calculate, ask them to state (not solve) which rule applies to 3 quick example triangles — checks rule-selection before computation errors can mask a conceptual gap.

Plenary / exit ticket (≈10 min)

A single multi-step problem: “A ship sails from port on a bearing of 065° for 40 km, then changes course to a bearing of 130° for 25 km. Find the distance and bearing back to port.” Requires sketching, cosine rule, and bearing interpretation — a genuine synthesis task.

Resources

GDC for rapid numerical checking (see Use of GDC in 2026.pdf); Haese AA SL textbook chapter M07 (Trigonometry) under IB DP Mathematics/PPT of SL Mathematics/.

Builds directly on the MYP5 sine/cosine-rule work (below); the area formula and multi-step bearings synthesis go beyond typical IGCSE depth, and the HL compound-angle preview sets up later DP identities work absent from MYP/IGCSE.

B. MYP Mathematics — Grade 10 (MYP Year 5)

Anchor concept: Sine and cosine rules and their applications (Spatial Reasoning branch, MYP5 Extended).

Prior knowledge assumed: Right-triangle trig ratios (SOH-CAH-TOA), Pythagoras’ theorem, bearings notation (MYP3/4).

Learning objectives

Assessment criteria addressed

Criterion A (Knowing and understanding) — correct selection and application of the appropriate rule; Criterion D (Applying mathematics in real-life contexts) — solving a real-world bearings or navigation problem and justifying the reasonableness of the answer (e.g. does the calculated distance make sense given the map/context).

Command terms used

Calculate, Apply, Justify (D-criterion — reasonableness of the answer in context), Construct (an accurate diagram/sketch from worded information).

ATL / skills focus

Thinking skills (deciding which rule fits a given triangle); self-management (careful, labelled diagram construction as a problem-solving strategy).

Starter (≈10 min)

Give students a real photo or sketch of a triangular plot of land with two sides and an included angle marked. Ask: “How could a surveyor find the third side without measuring it directly?”

Main teaching sequence (≈35 min)

  1. Introduce the sine rule with a clear diagram convention (side opposite each angle); worked example using the land-plot context or similar.
  2. Introduce the cosine rule for the SAS case; contrast directly with the sine-rule example so students see when each applies.
  3. Explicit rule-selection practice: a set of triangles with different given information (SSA, SAS, three sides) — students state which rule (or Pythagoras) applies before calculating.
  4. Real-life application task (Criterion D): a navigation or construction problem (e.g. a triangular park, or two boats’ distances from a lighthouse at given bearings) requiring students to sketch, select the rule, calculate, and justify whether their answer is sensible.

Formative assessment / check for understanding

Gallery walk: students post their diagram + rule choice for a shared problem on the board; class briefly reviews for correct rule selection before full calculation is checked.

Plenary / exit ticket (≈10 min)

“A field is triangular with sides 50m and 65m and an included angle of 72°. Find the length of the third side and the area of the field. Is your answer reasonable for a field this size?” (Direct Criterion D justification prompt.)

Resources

Printed/digital triangle diagrams and real-context photos; GDC for numerical checking.

Extends IGCSE’s sine/cosine rule mechanics (below) into more open, context-justified problems, and is the direct precursor to the DP C2 work above, which adds the area formula, ambiguous-case awareness, and (HL) compound-angle identities.

C. IGCSE Mathematics — Grade 10 (Extended tier)

Caveat: IGCSE content below follows standard Cambridge (0580) / Edexcel International GCSE (4MA1) Extended-tier syllabus content. No official board specification file was found on this machine — cross-check against the current specification before formal use.

Anchor concept: Sine rule, cosine rule, area of a triangle, and bearings.

Prior knowledge assumed: Right-triangle trig ratios, Pythagoras’ theorem, angle facts, basic bearings.

Learning objectives

Assessment objectives addressed

AO1 (recall and apply standard techniques — direct rule application); AO3 (solve problems in context — bearings and multi-step geometry problems).

Command terms used

Calculate, Find, Show that — standard Cambridge/Edexcel command-term conventions.

Starter (≈10 min)

Quick recap: right-triangle trig — find a side and an angle in two right triangles, timed. Then show a triangle with no right angle and ask what’s different.

Main teaching sequence (≈35 min)

  1. Sine rule: introduce the formula and side/angle labelling convention; worked example, then guided practice finding a side, then an angle.
  2. Cosine rule: introduce both forms (finding a side; rearranged for finding an angle); worked example and guided practice.
  3. Rule-selection practice: mixed set of triangles (SSA, SAS, SSS) — students must decide which rule applies before solving.
  4. Area formula (\frac{1}{2}ab\sin C); apply to 2–3 triangles, including one combined with a cosine-rule step (find a missing side first, then the area).
  5. Bearings problem: a two-leg journey problem (as in the DP starter above, but single-step) requiring sketching and one rule application.

Formative assessment / check for understanding

Mini-whiteboard check at each stage transition (after sine rule, after cosine rule) before moving on, to catch rule-confusion early.

Plenary / exit ticket (≈10 min)

“Triangle ABC has AB = 8cm, BC = 11cm, and angle ABC = 95°. Find AC and the area of triangle ABC.”

Resources

Past-paper style trigonometry questions (Extended tier); GDC for numerical checking.

Provides the sine/cosine-rule mechanics that MYP5 extends into open, justified real-world problems, and that DP AA extends further with the area formula in multi-step synthesis, the ambiguous case, and (HL) compound-angle identities.