Right-angled triangles

In the figure labelled $ABCDEF$, $BCD$ lies on one straight line, and $CA$ is parallel to $DF$. The angles $\angle ABD$, $\angle BDE$ and $\angle DEF$ are all right angles. Also, $AB = 4\text{ m}$, $DE = 11\text{ m}$ and $EF = 4\text{ m}$.

May/June 2015

Ports $A$ and $B$ are $15\text{ km}$ apart, with $B$ lying directly south of $A$. A boat sets off from $A$ on a bearing of $141^\circ$.

May/June 2015

AB is vertical, whereas CB is horizontal. $AB = 31\text{ m}$ and $CB = 115\text{ m}$. J and K are two points out at sea. The lighthouse has its base at L. J lies due East of L, while K lies due South of L. $KL = 354\text{ m}$ and $KJ = 1100\text{ m}$.

May/June 2016

The figure depicts a vertical wind turbine whose blades measure 30 m in length.

May/June 2016

Triangle $PQR$ is right-angled at $P$, with $\angle PRQ=38^\circ$ and $RQ=12\text{ cm}.$

May/June 2017

A boat departs from $A$ and covers $12\text{ km}$ to reach $B$.

May/June 2018

The diagram depicts an isosceles triangle $ABC$ with $AB = AC$. Point $D$ lies on $AC$ so that angle $ADB = 90^\circ$. Point $E$ lies on $AB$ so that angle $AEC = 90^\circ$.

May/June 2021

The diagram depicts an open-top container resting on a horizontal plane. The container is a prism, and trapezium $ABCD$ forms its cross-section. $AB = 28$ cm, $DC = 24$ cm, $AD = 16$ cm and $BF = 29$ cm. Angle $ADC$ and angle $DAB$ are right angles.

May/June 2023

$\cos y^\circ = -0.54$ with $90 \le y \le 180$. A solution of $\cos x^\circ = 0.54$ is $x = 57$, correct to the nearest whole number. Find $y$, correct to the nearest whole number.

Oct/Nov 2015

The diagram illustrates a vertical radio mast, $AB$. Three of the supporting wires are fixed to it at $F$, $H$ and $D$. The foot of the mast, $A$, and the far ends $E$, $G$ and $C$ of the wires lie on one straight line on horizontal ground.

Oct/Nov 2015

The diagram depicts a square-based pyramid. X marks the centre of the square base. Vertex E lies directly above X, and EX = 7 cm. The perpendicular height of triangle BEC is 11 cm.

Oct/Nov 2025

ABCD is a field, and a straight path runs across it from B to D. Diagram details: DB = 495 m, DC = 620 m, BC = 580 m, angle ABD = 42^{\circ}, angle DAB = 90^{\circ}.

Oct/Nov 2025