Right-angled triangles

A right-angled triangle ABC is drawn, and it is NOT TO SCALE. AB is vertical and measures 6.2 m, BC is horizontal and measures 13.8 m, the angle at B is a right angle, and the angle at C is marked $x\degree$.

Feb/March 2017

The diagram shows a right-angled triangle $ABC$, and it is NOT TO SCALE. The lengths are $AB = 1.6$m and $BC = 2.8$m, with the right angle at $B$.

Feb/March 2018

The diagram depicts triangles $ABC$ and $BCD$; each one is right-angled. The labelled lengths are $AC = 8.2\,$cm, $BC = 5.3\,$cm, $CD = y\,$cm, $BD = 4.4\,$cm, and the angle at A is marked $x^\circ$. The figure is not drawn to scale.

Feb/March 2019

Calculate the bearing from Alexandria to Paris.

Feb/March 2019

The diagram represents a right-angled triangle $ABC$. Here, $AC = 4.6\text{ m}$ and angle $C = 37\text{\u00b0}$. The diagram is marked NOT TO SCALE.

Feb/March 2020

The figure depicts a right-angled triangle. Its base is $74\text{ cm}$, its vertical height is $46\text{ cm}$, and the angle on the left is marked $y$. The figure is not drawn to scale.

Feb/March 2023

The sketch depicts quadrilateral $ABCD$. Also, $AC = 12.3$ cm and $AD = 16.5$ cm. In addition, angle $BAC = 31^\circ$, angle $ABC = 90^\circ$ and angle $ACD = 90^\circ$.

Feb/March 2023

The quadrilateral $ACDE$ is made up from two right-angled triangles, $ABE$ and $BCD$. The given lengths are $AC = 17$ cm, $AE = 18$ cm and $BD = 6$ cm, and the diagram shows an angle of $60^\circ$ at $A$.

Feb/March 2025

A right-angled triangle $ABC$ is drawn. Angle $ABC$ is a right angle, angle $ACB = 37^{\circ}$, and $AC = 11.2\,\text{cm}$. The diagram is labelled NOT TO SCALE.

May/June 2015

The sketch represents a right-angled triangle. Its base measures $2\text{ cm}$, the hypotenuse measures $5\text{ cm}$, and the angle at the end of the base is labelled $x^\circ$. The sketch is marked NOT TO SCALE.

May/June 2015

A right-angled triangle is drawn, and it is not to scale. The side marked 5 cm, the base marked 2 cm, and the acute angle at the base is $x^{\circ}$.

May/June 2015

A ramp, $AB$, is $23\text{ m}$ in length and rises at an angle of $16^{\circ}$ above the horizontal, $AC$.

May/June 2016

A right-angled triangle is drawn with a vertical side of $4$ cm, a hypotenuse of $7$ cm, and the base angle labelled $x^\circ$. The diagram is NOT TO SCALE.

May/June 2017

The diagram illustrates a right-angled triangle. One side measures $4\text{ cm}$, the hypotenuse measures $7\text{ cm}$, and the angle at the base is labelled $x^\circ$. The diagram is marked NOT TO SCALE.

May/June 2017

A right-angled triangle, shown NOT TO SCALE, has a base measuring 5 cm and a hypotenuse measuring 8 cm, and the angle at the left-hand end of the base is marked $x^\circ$.

May/June 2018

The diagram depicts a right-angled triangle. Its hypotenuse is 12 cm, one angle measures $35^\circ$, and the vertical side has been labelled $x$ cm. NOT TO SCALE.

May/June 2019

The diagram depicts a right-angled triangle with a side measuring 6.2 m, a hypotenuse measuring 23 m, and an angle $x^\circ$. The diagram is not drawn to scale.

May/June 2019

A vertical flagpole, BD, is set on horizontal ground and supported by two ropes, AD and CD. AD = 15 m, BC = 10.7 m and angle DAB = 38^{\circ}. The diagram is marked NOT TO SCALE.

May/June 2019

A right-angled triangle is drawn. One side measures 12 cm, the base angle is $35^{\circ}$, and the vertical side is marked $x$ cm. The figure is labelled NOT TO SCALE.

May/June 2019

The diagram depicts a right-angled triangle. One side has length $18\text{ cm}$, the hypotenuse measures $30\text{ cm}$ and the angle at the base is marked $x^\circ$. The diagram is labelled NOT TO SCALE.

May/June 2021

A triangle $ABC$ is drawn, with angle $C$ equal to $65^{\circ}$. The perpendicular distance from $B$ to $AC$ is $12.8\text{ cm}$.

May/June 2021

The diagram represents a right-angled triangle, $ABC$. $AC = 15$ cm and angle $BAC = 38^{\circ}$.

May/June 2022

The diagram illustrates two right-angled triangles, $ABD$ and $BCD$. $AD = 5$ m, $DC = 14$ m and angle $BAD = 53^{\circ}$. NOT TO SCALE.

May/June 2022

The figure shows two right-angled triangles, ABC and PQR. In triangle ABC, AB = $7.3\,\text{cm}$ and BC = $9.2\,\text{cm}$. In triangle PQR, RQ = $9.2\,\text{cm}$ and PQ = $7.3\,\text{cm}$.

May/June 2022

In triangle ABC, $AC = AB$. Point D lies on BC so that AD is perpendicular to BC. The diagram marks a right angle at D. NOT TO SCALE.

May/June 2022

The diagram depicts a right-angled triangle with sides 7.5 cm and 12.8 cm, and an angle marked $y^{\circ}$. It is labelled NOT TO SCALE.

May/June 2023

The sketch represents right-angled triangle $ABC$. Here $AB = (2x + 5)\text{ cm}$ and $AC = (x + 3)\text{ cm}$. The right angle is at $A$.

May/June 2023

In the diagram, a right-angled triangle has a side of 8.5 cm, a hypotenuse of 14 cm, and the base angle is marked $x^{\circ}$. The drawing is not to scale.

May/June 2024

The figure depicts a flagpole, BD, supported by two ropes, AD and CD. ABC lies on a straight line, and angle ABD = $90^{\circ}$. $AD=21.2$ m, $AB=16.5$ m and angle BCD = $48^{\circ}$. The diagram is not drawn to scale.

May/June 2024

The figure represents a right-angled triangle. In triangle $ABC$, $\angle A = 90^\circ$, $\angle B = 37^\circ$ and $CB = 8\text{ cm}$. The drawing is not drawn to scale.

May/June 2024

Calculate how long the ladder $GH$ is.

May/June 2024

The diagram depicts a right-angled triangle, $PQR$. $PQ = 6\text{ cm}$ and $PR = 8\text{ cm}$. The right angle is located at $Q$. The diagram is marked NOT TO SCALE.

May/June 2025

A right-angled triangle is shown. The vertical side has length 18.4 cm. One angle is 52^{\circ}. The base is labelled $y$ cm. The diagram is marked NOT TO SCALE.

May/June 2025

Triangle $ABC$ is drawn. $AB = 14.5\text{ m}$, $BC = 19.3\text{ m}$, and angle $A$ is a right angle. The diagram is marked NOT TO SCALE.

Oct/Nov 2015

A right-angled triangle is pictured. The vertical side is 2 cm long, the hypotenuse is 5 cm long, and the angle at the bottom is marked $x^{\circ}$. The diagram is marked NOT TO SCALE.

Oct/Nov 2015

A right-angled triangle is drawn with a vertical left side measuring 2 cm, a sloping hypotenuse measuring 5 cm, and the angle at the bottom right marked $x^\circ$. The diagram is not drawn to scale.

Oct/Nov 2015

The diagram depicts a right-angled triangle. The vertical side measures $15\text{ cm}$, the hypotenuse is labelled $x\text{ cm}$, and the angle at the base is $37^{\circ}$. The diagram carries the note NOT TO SCALE.

Oct/Nov 2016

A right-angled triangle is drawn. Its hypotenuse measures 14 cm, one angle is $32^\circ$, and the vertical side is marked $x$ cm. The diagram carries the label "NOT TO SCALE".

Oct/Nov 2016

Viewed from the top of a building that is $300\text{ m}$ tall, the angle of depression to a car, $C$, is $52^{\circ}$. A right-angled triangle is drawn with a vertical side of $300\text{ m}$, and at the top the angle between the vertical and the sloping line of sight is $52^{\circ}$. The figure is labelled "NOT TO SCALE".

Oct/Nov 2016

Work out $x$.

Oct/Nov 2016

The figure shows a right-angled triangle. Its left-hand vertical edge measures $6.4\,\text{cm}$. The slanted side, which is the hypotenuse, measures $8.1\,\text{cm}$. The angle between the bottom horizontal side and the hypotenuse is labelled $x^{\circ}$. The diagram is marked NOT TO SCALE.

Oct/Nov 2017

The diagram depicts triangle $ABC$. $ABC$ is a right-angled triangle. At $C$, the angle is $52^{\circ}$. The vertical side from $A$ to $B$ measures $8.6\text{ cm}$. The sketch is labelled NOT TO SCALE.

Oct/Nov 2017

A triangle’s angles are shared in the ratio 2 : 3 : 5.

Oct/Nov 2017

The diagram depicts a right-angled triangle.

Oct/Nov 2018

The sketch depicts a right-angled triangle ABC. AB measures $4(x-1)$ cm, while AC measures $(2x+5)$ cm. The triangle has area $30\text{ cm}^2$.

Oct/Nov 2018

The diagram, which is not drawn to scale, shows a right-angled triangle with base 12 cm, hypotenuse $x$ cm, and a $43^\circ$ angle at the base.

Oct/Nov 2019

A right-angled triangle is displayed. Its base measures 22 cm. The angle at the lower-right corner is $36^\circ$. The hypotenuse has been labelled $x$ cm. The diagram is labelled NOT TO SCALE.

Oct/Nov 2020

A right-angled triangle is shown. The sloping side measures 12 cm, the base is 7 cm, and the angle at the base is marked $x^{\circ}$. The diagram is not drawn to scale.

Oct/Nov 2021

Show that $BC = 75$ m.

Oct/Nov 2021

The figure depicts a right-angled triangle. One edge has length $17.5\text{ cm}$, an angle of $48^{\circ}$ is marked, and the hypotenuse is named $x\text{ cm}$. The drawing is not to scale.

Oct/Nov 2022

A right-angled triangle $ABC$ is shown. The hypotenuse measures 18 cm and the angle at $C$ is $42^\circ$. The diagram is marked NOT TO SCALE.

Oct/Nov 2022

The diagram represents a right-angled triangle. One of the angles is $56^\circ$, the hypotenuse measures $21.8\text{ cm}$ and the base measures $x\text{ cm}$. NOT TO SCALE.

Oct/Nov 2022

$ABC$ forms a right-angled triangle. NOT TO SCALE. $BC = 18\text{ cm}$, and the angle at $C$ is $34^\circ$.

Oct/Nov 2023

The diagram represents a right-angled triangle whose base is $5\,$cm, whose vertical side is $t\,$cm, and whose hypotenuse is $(2t+3)\,$cm. The angle at the left end of the base is marked $w^{\circ}$.

Oct/Nov 2023

The figure depicts a right-angled triangle. Its hypotenuse measures 9.7 cm. One acute angle is $42^{\circ}$. The side drawn vertically is marked $x$ cm.

Oct/Nov 2024

The diagram depicts a right-angled triangle ABC.

Oct/Nov 2025

ABC makes a right-angled triangle. The right angle is at A, angle B is 27^{\circ}, and AC measures 32 cm.

Oct/Nov 2025

The diagram depicts a right-angled triangle with a 12 cm base and a 37^{\circ} angle; the side opposite that angle is x cm.

Oct/Nov 2025

The diagram presents an isosceles triangle with a base of 4 cm and a perpendicular height of 5 cm. The two equal sides measure x cm.

Oct/Nov 2025

Calculate the angle of elevation of point T from point E.

Oct/Nov 2025