Non-right-angled triangles

For triangle $ABC$, $BC = 16\text{ cm}$ and $\angle BAC = 60^\circ$. The length of $AB$ is $x\text{ cm}$, and $AC$ measures $2x + 3\text{ cm}$.

May/June 2015

The diagram shows $AB=8\text{ cm}$, $AC=11\text{ cm}$ and $DC=6.5\text{ cm}$. Also, $\angle B\hat{A}D=26^\circ$ and $\angle D\hat{A}C=30^\circ$.

May/June 2015

$ABCD$ is the sloping rectangular face of the triangular prism. $ABEF$ forms a horizontal rectangle, and $EC$ and $DF$ are vertical. $\angle CBE = 15^\circ$, $DC = 5\text{ m}$ and $AD = 2\text{ m}$.

May/June 2016

A yacht travels around the triangular path shown. The bearing of $B$ from $A$ is $135^\circ$. $BC = 3.7\text{ km}$, $AC = 2.8\text{ km}$ and $\angle ABC = 42^\circ$.

May/June 2018

The diagram indicates the locations of ports $A$ and $B$, together with lighthouse $L$. From $L$, the bearing of $B$ is $062^\circ$. $AB = 13\text{ km}$, $BL = 14\text{ km}$ and $AL = 8\text{ km}$.

May/June 2019

The diagram depicts a triangular prism, with $AC = 15\text{ cm}$, $BC = 14\text{ cm}$, and $\angle ACB = 27^\circ$.

May/June 2019

The diagram indicates where the three towns, $A$, $B$ and $C$, are located.

May/June 2022

The pole $PQ$ is vertical. A rope goes from the top of the pole, $P$, to a point on the ground, $R$. Two more ropes are attached too.

May/June 2022

For triangle $ABC$, $AC = 8.3$ cm and $\angle BAC = 105^\circ$. The diagram also represents quadrilateral $PQRS$. Here $SQ = 15$ cm, $\angle SPQ = 67^\circ$ and $\angle PQS = 74^\circ$.

May/June 2023

A, B and C are points on flat ground. The bearing of $B$ from $A$ is $072^\f$. The bearing of $C$ from $A$ is $205^\f$. $AB = 170\text{ m}$ and $AC = 95\text{ m}$.

May/June 2023

Find the bearing from $B$ to $A$.

May/June 2024

The diagram depicts a pentagon.

May/June 2024

The diagram represents a triangular field $ABC$. Here, $AB = 150\text{ m}$, $BC = 187\text{ m}$, and $\angle ABC = 112^{\circ}$.

May/June 2025

The figure contains triangle $ABC$ along with triangle $ABD$. Here $AB = 12\text{ cm}$, $BD = 7\text{ cm}$ and $AD = 6\text{ cm}$. Also, angle $DAC = 32^{\circ}$ and angle $BCA = 48^{\circ}$.

May/June 2025

ABCDE is a pentagon that has one line of symmetry. $BC = DE = 10\text{ cm}$, $DC = 30\text{ cm}$ and $\angle BCD = \angle CDE = 90^\circ$. The minimum distance from $A$ to $DC$ is $22\text{ cm}$.

Oct/Nov 2015

The points $A$, $B$ and $D$ lie on one straight line, while $A$, $C$ and $E$ lie on another. $BD = 12\text{ cm}$ and $CE = 4\text{ cm}$. $AB = x\text{ cm}$ and $AC = (2x - 5)\text{ cm}$. Angle $BAC = \theta^{\circ}$.

Oct/Nov 2015

The sketch locates four islands at $A$, $B$, $C$ and $D$. $A$ lies due north of $B$. $\angle DAC = 48^\circ$, $\angle CAB = 55^\circ$ and $\angle BCA = 51^\circ$. $AC = 19\text{ km}$ and $AD = 27\text{ km}$.

Oct/Nov 2016

Within the quadrilateral $ABCD$, $BD=3\text{ m}$. Also, $\angle BDA=27^\circ$ and $\angle BCD=41^\circ$. The angles $\angle DBC$ and $\angle DAB$ are right angles.

Oct/Nov 2016

The diagram indicates the locations of the three towns, $A$, $B$ and $C$. $B$ lies due north of $A$, and the bearing of $C$ from $A$ is $220^\circ$. $AB = 25$ km and $AC = 38$ km.

Oct/Nov 2017

A prism is shown with a rectangular base measuring $15\text{ cm}$ by $x\text{ cm}$. Its cross-section is a right-angled triangle. The prism's height is $4\text{ cm}$ less than its width. The volume comes to $440\text{ cm}^3$.

Oct/Nov 2018

The diagram depicts a triangular field $ABC$. The lengths are $AB = 95\text{ m}$, $BC = 132\text{ m}$ and $AC = 174\text{ m}$.

Oct/Nov 2018

The diagram indicates the locations of three farms $A$, $B$ and $C$ on level ground. Farm $B$ lies on a bearing of $125^{\circ}$ from farm $A$. $AB = 950\,\text{m}$, $BC = 680\,\text{m}$ and $AC = 520\,\text{m}$.

Oct/Nov 2019

A quadrilateral field is labelled $PQRS$. A path runs across the field from $P$ to $R$. $PQ = 280$m, $RS = 146$m and $PR = 325$m. $S$ lies on a bearing of $042^\circ$ from $P$, $\angle PSR = 108^\circ$ and $\angle RPQ = 38^\circ$.

Oct/Nov 2019

$\sin x^\circ = \sin 50^\circ$ with $90 \le x \le 180$. Find $x$.

Oct/Nov 2022

The diagram indicates the locations of the three towns $P$, $Q$ and $R$.

Oct/Nov 2022

$ABCD$ forms a rectangular field. $C$ lies directly south of $A$. $AB = 450\,\text{m}$ and $BC = 210\,\text{m}$.

Oct/Nov 2023

The diagram presents triangle ABC as a triangular field. AB = 65 m, AC = 75 m and angle CAB = $125^\circ$.

Oct/Nov 2025