Your team has a different specialist tool. Learn it, teach it, then use the right tool to solve the whole mission.
01 · Become expert02 · Teach team03 · Choose & solve04 · Prove it alone
Step 01
Choose your expert field team
Select the role your teacher assigned. You will start with one applied problem, then carry that expertise into your mixed team.
Your choice is stored on this device. You can change it at any time.
Step 02 · Expert work
Your field briefing
EXPERT TIME Start when your teacher says go.
Area Surveyor
Briefing: shade for the courtyard
A triangular shade structure has side lengths 18 m and 24 m, with an included angle of 53°. The fabric supplier charges RM36 per m².
Draw and label a triangle. Identify the two known sides and the included angle.
Choose the correct rule. Explain why it is more useful than base × height here.
Find the area of fabric required, then estimate the cost.
Your teach-back: “Use this rule when …”
Check: A = ½(18)(24) sin 53° ≈ 172.5 m². Cost ≈ RM6,210. The perpendicular height is unavailable, but two sides and their included angle are known.
Triangulation Specialist
Briefing: swimmer safety zone
Lifeguard points A and B are 120 m apart. A swimmer at C is observed at an angle of 58° from A and 47° from B. A rescue boat is stationed at B.
Sketch the situation and find the third angle.
How far is the swimmer from B?
The rescue-zone radius is 100 m. Is the swimmer inside it?
Your teach-back: “Use this rule when …”
Check: ∠C = 75°. BC = (120 sin 58°) / sin 75° ≈ 105.3 m. The swimmer is outside the rescue zone. A known side and its opposite angle pair unlock the sine rule.
Route Designer
Briefing: zip-line connection
Two access paths from a starting point are 31 m and 26 m, with an included angle of 38°. A zip line will connect their endpoints.
Sketch and label the direct zip-line distance.
Choose the correct rule and calculate the distance.
Cables are supplied only in whole metres. What minimum length should be ordered?
Your teach-back: “Use this rule when …”
Check: c² = 31² + 26² − 2(31)(26) cos 38°, so c ≈ 19.2 m. Order 20 m. Two sides and their included angle unlock the cosine rule when the missing side is needed.
The answer check unlocks seven minutes after the timer starts. Use it to verify your expertise, not replace your reasoning.
Field manual · use after expert work
Rule-selection map
Known information
What you need
Tool
Two sides and the included angle
Area
A = ½ab sin C
A side and its opposite-angle pair
A missing side or angle
a / sin A = b / sin B
Two sides and the included angle
The third side
c² = a² + b² − 2ab cos C
Step 03 · Mixed team mission
Three decisions. Three tools.
Your mixed group should contain one expert from each field team. Before calculating, every question needs a written rule choice and reason.
Mission A
Festival food-truck zone
A triangular zone has sides 14 m and 22 m, with an included angle of 61°. Find its area.
First write: Rule: ______ because ______.
Interpretation: How much temporary flooring is required?
Area rule. A = ½(14)(22) sin 61° ≈ 134.7 m².
Mission B
Coastal distance check
In triangle ABC, A = 42°, B = 71°, and a = 85 m. Find b.
First write: Rule: ______ because ______.
Interpretation: Which side is opposite the 71° angle?
Sine rule. b = (85 sin 71°) / sin 42° ≈ 120.1 m.
Mission C
Roof-truss connection
Two roof beams are 17 m and 24 m, meeting at an angle of 68°. Find the third side of the truss.
First write: Rule: ______ because ______.
Interpretation: Explain why the cosine rule fits this triangle.
Cosine rule. c = √[17² + 24² − 2(17)(24) cos 68°] ≈ 23.6 m.
Step 04 · Individual checkpoint
Prove you can choose the tool
Complete these independently in your notebook or on paper. Write the rule first, then your reason and calculation.
1
Area
A triangular banner has sides 11 cm and 16 cm with included angle 42°. Which rule? Find its area.
Write: rule → reason → calculation → units
2
Choose only
You know two sides and a non-included angle. Can you use the area rule immediately? Explain.
Write: yes or no → explain using “included angle”
3
Missing side
Two sides are 8 m and 13 m, with an included angle of 57°. Which rule finds the third side?
Write: rule → reason; calculate if your teacher asks
Finish: Show your three written responses to your teacher for feedback.