Right-angled triangles: past paper questions

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• Question 7May/June 2026, paper 21Structured2 marks

  The diagram shows the positions of three ships $P$, $Q$ and $R$. Ship $Q$ is $40\text{ km}$ due east of ship $R$. Ship $P$ is $40\text{ km}$ due north of ship $Q$.

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• Question 10Oct/Nov 2025, paper 23Structured4 marksHas a diagram

  The diagram shows a right-angled triangle $ABC$. Work out the exact length of $AC$.

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• Question 20Oct/Nov 2024, paper 21Structured5 marksHas a diagram

  The diagram shows two right-angled triangles $PQS$ and $RQT$. $PQR$ and $QTS$ are straight lines. Calculate angle $QTR$.

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• Question 18Oct/Nov 2023, paper 21Structured3 marksHas a diagram

  Calculate the value of $y$.

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• Question 11May/June 2026, paper 42Structured2 marks

  Calculate $XY$.

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• Question 13Oct/Nov 2025, paper 41Structured3 marksHas a diagram

  The diagram shows two vertical poles, $AE$ and $PT$, standing on horizontal ground, $AP$. Calculate the angle of elevation of the point $T$ from the point $E$.

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• Question 16Oct/Nov 2024, paper 23Structured3 marks

  Calculate the shortest distance from $C$ to $AB$.

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• Question 21Oct/Nov 2023, paper 21Structured4 marksHas a diagram

  The diagram shows a cuboid $ABCDEFGH$. $AB=15.1\text{ cm}$, $BC=4.5\text{ cm}$ and $CG=9.2\text{ cm}$. Calculate the angle that the diagonal $BH$ makes with the face $ADHE$.

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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 18Oct/Nov 2025, paper 43Structured6 marksHas a diagram

  Calculate the value of $x$.

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• Question 22Oct/Nov 2024, paper 23Structured4 marksHas a diagram

  The diagram shows a cuboid with a diagonal $PB$. Calculate the angle between the diagonal $PB$ and the base $ABCD$.

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• Question 21Oct/Nov 2023, paper 23Structured6 marks

  The diagram shows a cuboid $ABCDEFGH$. $AB=14\text{ cm}$, $BC=5\text{ cm}$ and $CG=8\text{ cm}$. $M$ is the midpoint of $HG$.

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• Question 7May/June 2026, paper 43Structured5 marks

  The point $A$ is on the top of a vertical building. The horizontal distance from the base of the building to $B$ is $22\text{ m}$. $AB=25\text{ m}$ and the height of the building is $h\text{ m}$.

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• Question 20May/June 2025, paper 21Structured4 marksHas a diagram

  Find the exact value of $x$.

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• Question 9Oct/Nov 2024, paper 41Structured12 marksHas a diagram

  $ABCDEFGH$ is a solid cuboid. $AB=10\text{ cm}$, $BC=8\text{ cm}$ and $CG=17\text{ cm}$. Work out the volume of the cuboid.

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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 23May/June 2025, paper 23Structured6 marksHas a diagram

  Write down the value of $\cos {90}^{\circ }$.

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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 6Oct/Nov 2023, paper 42Structured7 marks

  The diagram shows a right-angled triangle. Find the value of $w$.

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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 21May/June 2024, paper 21Structured4 marksHas a diagram

  The diagram shows a cuboid. $HD=4\text{ cm}$, $EH=6.5\text{ cm}$ and $EF=9.1\text{ cm}$. Calculate the angle between $CE$ and the base $CDHG$.

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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 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 12May/June 2024, paper 22Structured2 marksHas a diagram

  The diagram shows a right-angled triangle. Calculate the value of $x$.

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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 9May/June 2024, paper 23Structured2 marksHas a diagram

  The diagram shows a right-angled triangle. Calculate $AB$.

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• Question 3May/June 2023, paper 42Structured13 marks

  The diagram shows a right-angled triangle $ABC$. The area of the triangle is $60{\text{ cm}}^2$. Show that $2x^2+11x-105=0$.

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• Question 24May/June 2024, paper 23Structured4 marksHas a diagram

  The diagram shows a triangular prism with cross-section triangle $BCV$. Angle $BCV={90}^{\circ }$, $BC=5\text{ cm}$, $CV=4\text{ cm}$ and $AB=15\text{ cm}$. Calculate the angle between $AV$ and the base $ABCD$.

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• Question 10May/June 2023, paper 42Structured8 marksHas a diagram

  $ABCDEFGH$ is a cuboid with a square base of side $x\text{ cm}$. $CG=20\text{ cm}$ and $AG=28\text{ cm}$. Calculate the value of $x$.

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