Non-right-angled triangles: past paper questions

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• Question 20May/June 2026, paper 42Structured10 marksHas a diagram

  The diagram shows a field $ABCD$ with a straight footpath from $A$ to $C$. Find the bearing of $A$ from $B$.

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• Question 23Oct/Nov 2025, paper 23Structured3 marks

  Work out the area of triangle $ABC$.

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• Question 6Oct/Nov 2024, paper 41Structured11 marksHas a diagram

  The diagram shows a field $ABCD$. A straight path $AC$ goes across the field. Show that $AC=1028\text{ m}$, correct to the nearest metre.

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• Question 19Oct/Nov 2023, paper 23Structured4 marksHas a diagram

  Calculate the obtuse angle $PRQ$.

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• Question 8May/June 2026, paper 43Structured5 marksHas a diagram

  $AB$ and $CD$ are parallel lines. $AD$ and $BC$ are straight lines that intersect at $X$. Angle $ABX=y^{\circ }$.

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• Question 21Oct/Nov 2025, paper 41Structured2 marks

  In triangle $STU$, $ST=8\text{ cm}$, $SU=9\text{ cm}$ and angle $TSU={50}^{\circ }$. Calculate the area of triangle $STU$.

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• Question 7Oct/Nov 2024, paper 42Structured20 marksHas a diagram

  The diagram shows a field, $ABCD$ with $B$ north of $A$. $BD$ is a path across the field. $AB=85\text{ m}$, $AD=72\text{ m}$, $BD=129\text{ m}$, angle $BDC={39}^{\circ }$ and angle $BCD={60}^{\circ }$.

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• Question 5Oct/Nov 2023, paper 41Structured14 marksHas a diagram

  $ACD$ is a right-angled triangle. $B$ is on $AC$ and $BC=54.5\text{ m}$. $AD=83.2\text{ m}$ and angle $ABD={38}^{\circ }$.

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• Question 13May/June 2026, paper 43Structured7 marksHas a diagram

  The diagram shows triangle $ABC$. $BC=15\text{ cm}$, $AC=15\sqrt{3}\text{ cm}$ and angle $ABC={120}^{\circ }$. Show that triangle $ABC$ is an isosceles triangle.

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• Question 29Oct/Nov 2025, paper 41Structured8 marksHas a diagram

  Calculate the value of $y$.

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• Question 12Oct/Nov 2024, paper 43Structured10 marksHas a diagram

  $ABCD$ is a quadrilateral and $E$ is a point on $CD$. $AB=8.7\text{ cm}$, $BC=11.4\text{ cm}$ and $CE=10.9\text{ cm}$. Angle $ADE={90}^{\circ }$, angle $ABC={119}^{\circ }$ and angle $CAE={20}^{\circ }$.

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• Question 7Oct/Nov 2023, paper 42Structured16 marksHas a diagram

  The diagram shows a right-angled triangle $PQR$ on horizontal ground. $X$ is vertically above $R$ and the angle of elevation of $X$ from $P$ is ${21}^{\circ }$. $XR=2.8\mathrm{m}$ and $RQ=7.1\mathrm{m}$.

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• Question 15May/June 2026, paper 43Structured3 marks

  The sides of a triangle are $5\text{ cm}$, $7\text{ cm}$ and $11\text{ cm}$. Find the size of the largest angle in this triangle.

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• Question 15Oct/Nov 2025, paper 42Structured10 marks

  The diagram shows a field, $ABCD$, in the shape of a quadrilateral. $BD$ is a straight path across the field. Calculate $BC$.

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• Question 17May/June 2024, paper 21Structured2 marks

  Calculate the area of triangle $ABC$.

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• Question 8Oct/Nov 2023, paper 43Structured17 marksHas a diagram

  The diagram shows a shape made from a major sector $AOB$ and triangles $OBC$ and $AOD$. $OB=6\text{ cm}$, $BC=2\text{ cm}$, obtuse angle $AOC={135}^{\circ }$ and angle $BCO={90}^{\circ }$. Show that angle $BOC={19.5}^{\circ }$, correct to 1 decimal place.

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• Question 12May/June 2025, paper 41Structured3 marksHas a diagram

  The diagram shows triangle $PQR$. Calculate the shortest distance from $Q$ to $PR$.

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• Question 6May/June 2024, paper 41Structured17 marksHas a diagram

  The diagram shows the positions of two lighthouses $A$ and $B$, a boat $C$ and a harbour $H$. $C$ is due east of $B$. Find the bearing of the harbour from boat $C$.

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• Question 17May/June 2023, paper 22Structured2 marks

  The diagram shows a triangle with an acute angle marked $x^{\circ }$. The area of the triangle is $2143{\mathrm{c}\mathrm{m}}^2$. Work out the value of $x$.

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• Question 17May/June 2025, paper 41Structured10 marksHas a diagram

  The diagram shows a quadrilateral $ABCD$. Calculate $AD$.

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• Question 6May/June 2024, paper 42Structured10 marksHas a diagram

  $ABCD$ is a quadrilateral with $AB=10.4\text{ cm}$ and $AD=6.5\text{ cm}$. Angle $DAB={64}^{\circ }$, angle $BDC={26}^{\circ }$ and angle $DBC={42}^{\circ }$. Show that $BD=9.55\text{ cm}$, correct to 2 decimal places.

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• Question 2May/June 2023, paper 41Structured16 marksHas a diagram

  The diagram shows a solid triangular prism $ABCDEF$ of length $15\text{ cm}$. $AB=6.4\text{ cm}$, $EB=5.7\text{ cm}$ and the volume of the prism is $145{\text{ cm}}^3$. Show that angle $EBA={32}^{\circ }$, correct to the nearest degree.

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• Question 20May/June 2025, paper 42Structured13 marksHas a diagram

  The diagram shows a quadrilateral $ABCD$. $CD=10\text{ m}$ and $DB=12\text{ m}$. Angle $DBA={90}^{\circ }$, angle $CDB={56}^{\circ }$ and angle $ADB={34}^{\circ }$.

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• Question 6May/June 2024, paper 43Structured15 marksHas a diagram

  The diagram shows a ladder, $GH$, on horizontal ground, leaning against a vertical wall, $HF$. $GF=1.5\text{ m}$ and $HF=4\text{ m}$. Calculate the length of the ladder, $GH$.

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• Question 4May/June 2023, paper 41Structured14 marksHas a diagram

  Calculate the area of triangle $PQR$.

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• Question 7May/June 2023, paper 42Structured11 marksHas a diagram

  The diagram shows the straight roads between town $A$, town $B$ and town $C$. $AC=60\text{ km}$, $CB=87\text{ km}$ and $B$ is due east of $A$. The bearing of $C$ from $A$ is ${038}^{\circ }$.

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• Question 5May/June 2023, paper 43Structured12 marksHas a diagram

  $ABC$ is a scalene triangle on horizontal ground. $AYX$ is a straight vertical post, held in place by two straight wires $XB$ and $YC$. $AC=4.8\text{ m}$, $BC=5.6\text{ m}$ and angle $ACB={20.4}^{\circ }$.

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