lesson
The included angle supplies a height
1 · Learn
For two sides a and b enclosing angle C, triangle area is ab sin C / 2. This follows by expressing a perpendicular height using sine. The angle must be the one between the two stated sides.
Keep area units squared and distinguish an exact trigonometric value from a rounded calculator result. An unrelated angle cannot simply be inserted.
2 · Worked example
Sides 6 cm and 8 cm enclosing 30° give area 6 × 8 × 0.5 / 2 = 12 cm².
3 · Your turn
Find area for sides 5 cm and 10 cm enclosing 30°.
Check your answer
12.5 cm².
4 · Apply your learning
Draw the perpendicular height and derive the formula from half base times height.
Adult guidance and safety
This sequence includes extension mathematics and assumes secure earlier work. Check prerequisite understanding and the learner's readiness before assigning extension tasks. Require derivations, accurate diagrams and varied practice; a correct short example is not full assessment evidence. Exam-board and tier-specific pathways are outside this edition.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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