Pythagoras' theorem and trigonometry in 3D

The diagram depicts a sketch of quadrilateral $ABCD$.

May/June 2021

The diagram depicts a pyramid $ABCV$. Its base is the equilateral triangle $ABC$, with each side measuring $34\text{ cm}$. The perpendicular height $VO$ meets the base at right angles. Also, $VA = VB = VC = 82\text{ cm}$.

May/June 2025

The building’s four walls make up the faces of cuboid $ABCDEFGH$. Because $T$ is positioned vertically above $C$ and $G$, $\angle ABT = \angle ADT = 90^\circ$. The cuboid is $9\text{ m}$ long, $8\text{ m}$ wide and $5\text{ m}$ high. $TC = 6\text{ m}$.

Oct/Nov 2016

A vertical mast, $XY$, stands on horizontal ground. Four cables hold the mast, each fixed to the mast at $P$ and to the ground at points $A$, $B$, $C$ and $D$. $Y$ is the centre of square $ABCD$. $PY = 7.50\text{ m}$.

Oct/Nov 2017

The diagram depicts a pyramid with a rectangular base lying horizontally. Vertex $F$ of the pyramid is directly above the centre of the base, $E$. $AB = 6.2\,\text{cm}$ and $BC = 4.3\,\text{cm}$. Each sloping edge of the pyramid measures $9.5\,\text{cm}$.

Oct/Nov 2018

Applying trigonometry to triangles and pyramids.

Oct/Nov 2020

A cuboid is shown in the diagram. $EH = 6$ cm, $HG = 2$ cm and $EC = 7$ cm.

Oct/Nov 2024

The cuboid is shown in the diagram. $EH=12$ cm, $HG=10$ cm and $GC=7$ cm.

Oct/Nov 2025