CAIE IGCSE Maths Extended 3D Geometry Overview

Practise solving 3D geometry problems with Pythagoras and trigonometry, including cuboids, prisms, rods and line-plane angles.

Exam points

build right triangles in cuboids or prisms to calculate diagonals and lengths
identify the angle between a line and a plane before applying trigonometry

Covered syllabus points

E6.6.1 in 3D Carry out calculations and solve problems in three dimensions

[Maximum number: 5]

NOT TO SCALE

The diagram shows triangle ABC on horizontal ground.
$A C=15 \mathrm{~m}, B C=8 \mathrm{~m}$ and $A B=20 \mathrm{~m}$ .
BP and CQ are vertical poles of different heights.
$B P=3 \mathrm{~m}$ and $C Q=4 \mathrm{~m}$ .
AQ and PQ are straight wires.

Another straight wire connects A to the midpoint of PQ.

Calculate the angle between this wire and the horizontal ground.

11.5 nfww or 11.48 to 11.49...
B1 for height 3.5
M2 for $15^2+4^2-2\times15\times4\cos117.5^\circ$
M1 for $\tan=\frac{3.5}{\text{their }17.216...}$ oe

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Covered syllabus points

E6.6 Pythagoras’ theorem and trigonometry question 1