Non-right-angled triangles

A triangle $PQR$ is illustrated, NOT TO SCALE. $PQ = 2.8$ cm, $QR = 8.3$ cm, and the angle at $Q$ is $79^\circ$.

Feb/March 2017

In triangle $TXZ$, the side $TX$ measures $12.5$ cm and angle $TZX$ is $37^\circ$. Point $Y$ lies on line $XZ$ so that $TY = 9.9$ cm, angle $XTY = 23^\circ$ and angle $TYZ = 72^\circ$.

Feb/March 2017

The sketch features the two ports $L$ and $P$ together with a buoy, $M$. From $P$, the bearing to $L$ is $201^\circ$ and $LP = 248$ km. From $P$, the bearing to $M$ is $127^\circ$. Angle $PML = 42^\circ$.

Feb/March 2018

The figure represents quadrilateral $PQRS$, which is made up of triangles $PQS$ and $QRS$. The marked angles are $25^\circ$ at $S$ between $SP$ and $SQ$, $72^\circ$ at $R$, and $34^\circ$ at $Q$ between $QS$ and $QP$. Also, $PQ = 7.4$ cm and $QS = 6$ cm. Diagram is NOT TO SCALE.

Feb/March 2020

The diagram depicts quadrilateral $ABCD$, together with the lengths and angles that are given.

Feb/March 2021

Calculate the triangle’s area.

Feb/March 2023

The figure shows triangle $ABC$ with $AB = 4.9$ cm, $BC = 5.6$ cm, and angle $ABC = 23^\circ$. It is labelled NOT TO SCALE.

Feb/March 2024

The diagram represents triangle $ABC$ with $AB=17.2$ cm. The angle at $B$ is $54^\circ$ and the angle at $C$ is $68^\circ$.

Feb/March 2024

The diagram places three points $A$, $B$ and $C$ on level ground. The bearing of $C$ from $A$ is $145^\circ$ and $\angle ACB = 38^\circ$. Also, $AC = 65\text{ m}$ and $BC = 95\text{ m}$. A north arrow is included. The diagram is marked NOT TO SCALE.

Feb/March 2025

A triangle $ABC$ is drawn, not to scale. The angle at $A$ measures $30^{\circ}$, the angle at $C$ measures $100^{\circ}$, and $AB = 24$ cm.

May/June 2015

Triangle $PQR$ is drawn here (not to scale). Given $PQ = 10$ cm and $PR = 9$ cm, the area of triangle $PQR$ is $38.5\,\text{cm}^2$.

May/June 2015

Ship positions and bearings.

May/June 2015

The diagram displays triangle $ABC$ with $AB = 7$ cm, $BC = 10$ cm and angle $ABC = 35^{\circ}$. It is not drawn to scale.

May/June 2016

A plane travels from A to C, then continues from C to B. $AC = 510$ km and $CB = 720$ km. The bearing of C from A is $135^\circ$ and angle $ACB = 40^\circ$.

May/June 2016

The figure shows a triangle in which $CB = 8.15\text{ m}$, the angle at $A$ is $110^\circ$, and the angle at $B$ is $30^\circ$. It is labelled NOT TO SCALE.

May/June 2017

For triangle $PQR$, $PQ = 8\text{ cm}$ and $QR = 7\text{ cm}$. Its area is $17\text{ cm}^2$.

May/June 2017

A triangle is drawn with sides measuring 24 cm and 39 cm, together with one angle of $71.8^{\circ}$ and the angle at the opposite vertex labelled $x^{\circ}$. The diagram is not drawn to scale.

May/June 2017

A, B and C name three towns. The bearing of B from A is 110^{\circ}. The bearing of C from B is 280^{\circ}. AC = 38 km and AB = 50 km.

May/June 2017

ABC is a triangular field on horizontal ground. A vertical pole BQ stands at B. $AB = 525$ m, $BC = 872$ m and angle $ABC = 104^{\circ}$.

May/June 2017

Triangle $ABC$ is drawn. $AC = 5.9\text{ cm}$ and $AB = 17.8\text{ cm}$. The angle at $C$ measures $84.6^{\circ}$. The diagram is labelled NOT TO SCALE.

May/June 2018

A triangle $LMN$ is drawn. The lengths are $LN = 14\text{ cm}$, $NM = 16\text{ cm}$ and $LM = 19\text{ cm}$. The figure is labelled NOT TO SCALE.

May/June 2018

A triangle sketch, drawn not to scale, has sides of $11\text{ cm}$ and $5\text{ cm}$ with a base of $13\text{ cm}$. The angle at the top, between the two sloping sides, is marked $x\degree$.

May/June 2018

The sketch depicts field ABCDE. The edge lengths and dotted interior lines are labelled as follows: $AB = 100$m, $BC = 170$m, $DE$ and $EA$ are also indicated, with $EA = 50$m. Within the field, dashed segments show $AD = 120$m and $BD = 150$m. Right-angle symbols appear at A and D. A north arrow points upwards. The diagram is NOT TO SCALE.

May/June 2019

Diagram (a): The triangles $ABD$ and $BCD$ are shown with their sides and angles marked. $AD = 16.5$ cm, $BD = 12.4$ cm, angle $ADB = 64^{\circ}$, angle $BDC = 53^{\circ}$, angle $DBC = 95^{\circ}$. Not drawn to scale. Diagram (b): A circular sector with radius 3.8 cm is shown. The arc length measures 7.7 cm, and the angle at the centre is labelled $y^{\circ}$. Not drawn to scale.

May/June 2019

Show that $AC=76.7\text{ m}$, accurate to 1 decimal place.

May/June 2019

The side lengths of a triangle are 11 cm, 10 cm and 9 cm.

May/June 2021

The diagram represents triangle $ABC$. Point $X$ lies on $BC$. $AX = 10.6$ cm, $XC = 6.4$ cm, angle $ABC = 58^{\circ}$ and angle $AXB = 78^{\circ}$.

May/June 2021

The diagram depicts quadrilateral $ABCD$, which is formed by triangles $ABD$ and $BCD$.

May/June 2021

Calculate the angle $ACD$.

May/June 2022

The diagram represents trapezium $ABCD$ (not drawn to scale), with $DC$ parallel to $AB$. Here, $DC = 6.4\,\text{cm}$, $DB = 10.9\,\text{cm}$, angle $CDB = 38^{\circ}$ and angle $DAB = 45^{\circ}$.

May/June 2022

The diagram places three towns, $U$, $V$ and $W$, on a map. $U$ lies exactly to the west of $V$, and angle $UVW = 125^\circ$. The distances labelled are $UV = 27.3\text{ km}$ and $UW = 62.4\text{ km}$. At $W$ there is a north arrow. Diagram marked NOT TO SCALE.

May/June 2023

The diagram depicts a triangle in which an acute angle is labelled $x^{\circ}$. Its area is $2143\text{ cm}^2$. The sides of the triangle are marked $92.5\text{ cm}$ and $71\text{ cm}$.

May/June 2023

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

May/June 2023

In the diagram, the locations of two lighthouses $A$ and $B$, a boat $C$ and a harbour $H$ are shown. $C$ lies due east of $B$.

May/June 2024

ABCD is a quadrilateral in which $AB = 10.4\,\text{cm}$ and $AD = 6.5\,\text{cm}$. Angle $DAB = 64^{\circ}$, angle $BDC = 26^{\circ}$ and angle $DBC = 42^{\circ}$.

May/June 2024

For this question, every measurement is in centimetres. The diagram depicts a triangle with sides $r+2$ and $r+5$ and a $30^{\circ}$ angle, together with a square of side $r+1$ (NOT TO SCALE). The triangle's area is the same as the square's area.

May/June 2024

The diagram depicts triangle $PQR$ with $PQ = 12.5\text{ cm}$, angle $\angle P = 42^\circ$ and angle $\angle Q = 115^\circ$. The figure is not drawn to scale.

May/June 2025

The diagram presents quadrilateral $ABCD$ with $AB = 9.6\text{ cm}$, $BC = 15.8\text{ cm}$, diagonal $BD = 12.1\text{ cm}$, angle at $B = 56^\circ$, and angle at $C = 47^\circ$. The figure is not drawn to scale.

May/June 2025

A triangle is drawn and it is not to scale. Its base measures $12.4\text{ cm}$. The side on the left is $y\text{ cm}$. The angle at the top is $74\degree$, while the angle at the bottom right is $39\degree$.

Oct/Nov 2015

Points A, B and C lie on horizontal ground. BT is a vertical pole. AT = 60 m, AB = 50 m, BC = 70 m and angle ABC = 130^{\circ}.

Oct/Nov 2015

The diagram indicates the distances between Mumbai (M), Kathmandu (K), Dhaka (D) and Colombo (C).

Oct/Nov 2015

For part (a), triangle ABC has sides AB = 6.2 cm and BC = 4.7 cm, with angle ABC = 82^{\circ}. The diagram is NOT TO SCALE. For part (b), triangle DEF has sides DE = 107 mm and DF = 75 mm, and the angle at D is marked $x^\circ$. The area of triangle DEF is 2050 mm$^2$. The diagram is NOT TO SCALE.

Oct/Nov 2016

The diagram represents a field, $ABCD$. In it, $AD = 180\,\text{m}$ and $AC = 240\,\text{m}$. In addition, angle $ABC = 50^{\circ}$ and angle $ACB = 85^{\circ}$.

Oct/Nov 2016

The diagram indicates the locations of a port, $A$, and a lighthouse, $L$. The circle with centre $L$ and radius 40 km marks the area from which the lighthouse’s light is visible. The straight line, $ABCD$, is the route followed by a ship after it departs from the port. At position $B$, the ship is directly west of the lighthouse. $AL = 92.1\text{ km}$, $AB = 61.1\text{ km}$ and $BL = 40\text{ km}$.

Oct/Nov 2016

A triangle $ABC$ is drawn, and it is not to scale. $AB = 5.9\text{ cm}$, $BC = 12.6\text{ cm}$, and angle $A = 79^\circ$.

Oct/Nov 2017

The diagram indicates where three cities are located: Geneva (G), Budapest (B) and Hamburg (H).

Oct/Nov 2018

A quadrilateral ABCD is drawn with the side lengths and angles already given.

Oct/Nov 2018

The diagram shows a triangle, NOT TO SCALE. Two sides measure 11 cm and 13 cm, and the angle enclosed by them is $39^{\circ}$.

Oct/Nov 2019

A triangle is drawn, and it is NOT TO SCALE. The side lengths are marked 8 cm and 12 cm, and one angle measures $39^{\circ}$. The obtuse angle is labelled $x$.

Oct/Nov 2019

The figure depicts a triangular field, $ABC$, laid out on level ground. An arrow indicates north. The side lengths are $AB = 120\text{ m}$, $AC = 150\text{ m}$ and $BC = 180\text{ m}$. The diagram is NOT TO SCALE.

Oct/Nov 2019

The figure depicts triangle $ABC$.

Oct/Nov 2019

The sketch depicts a field, $ABCD$, on level ground. The sides are marked as $AB = 158\text{ m}$, $BC = 107\text{ m}$, $CD = 86\text{ m}$, and the diagonal $AC = 132\text{ m}$. The angle at $D$ is $116^\circ$. A north arrow is drawn at $A$. Diagram not to scale.

Oct/Nov 2019

A triangle is drawn with one side measuring 8 cm, the base measuring 9 cm, the angle at the top equal to $100^\circ$, and the lower-right angle marked as $x^\circ$. The figure is not drawn to scale.

Oct/Nov 2020

The figure depicts a field, $ABCD$, set on level ground. The side lengths are $BC = 192$ m, $CD = 287.9$ m, $BD = 168$ m and $AD = 205.8$ m.

Oct/Nov 2020

ABCDE forms a pentagon.

Oct/Nov 2021

In triangle $ABC$, $AB = 7\text{ cm}$, angle $A = 115^{\circ}$ and angle $B = 35^{\circ}$. The diagram is not drawn to scale.

Oct/Nov 2022

The figure places ships A, B and C on a map. $AC = 17.6$ km, $BC = 12.8$ km and $\angle BAC = 25^{\circ}$. The bearing of C from B is $112^{\circ}$, while $\angle ABC$ is obtuse. Diagram NOT TO SCALE.

Oct/Nov 2022

The diagram shows a triangle with sides of $8.3\,$cm and $16.2\,$cm, together with an angle of $105^{\circ}$. The angle left unknown is marked $y^{\circ}$.

Oct/Nov 2023

The diagram represents triangle $PRQ$. $PQ = 18$ cm, $RQ = 13.5$ cm, and angle $RPQ = 42^{\circ}$. The diagram is NOT TO SCALE.

Oct/Nov 2023

Calculate the angle of elevation of $X$ from $Q$.

Oct/Nov 2023

The diagram of triangle ABC has AB = 20.3 cm, AC = 17.2 cm, BC = 11.1 cm, and the angle at A is $33.14^\circ$. The figure is marked "NOT TO SCALE".

Oct/Nov 2024

The diagram depicts a field $ABCD$. A straight route $AC$ cuts across the field. The given measurements are $AB = 1150\text{ m}$, $AD = 420\text{ m}$, $DC = 830\text{ m}$, angle $DAB = 106^\circ$ at $D$ and angle $ABC = 62^\circ$. The diagram is not drawn to scale.

Oct/Nov 2024

Show that angle $CBD = 81^\circ$.

Oct/Nov 2024

ABCD is a quadrilateral, with $E$ lying on $CD$. $AB=8.7$ cm, $BC=11.4$ cm and $CE=10.9$ cm. Also, $\angle ADE=90^\circ$, $\angle ABC=119^\circ$ and $\angle CAE=20^\circ$.

Oct/Nov 2024

Triangle STU has ST = 8 cm, SU = 9 cm and angle TSU = 50^{\circ}.

Oct/Nov 2025

The diagram represents field ABCD, which has the form of a quadrilateral. BD is a straight route across the field. AB = 180 m, BD = 300 m, DC = 112 m and angle BDC = $140^\circ$.

Oct/Nov 2025