Edexcel IGCSE Math B 9.B 2D and 3D trigonometry

Practise 2D and 3D trigonometry by locating the relevant triangle, finding missing lengths and choosing the correct trig rule.

Exam points

Use sine rule, cosine rule or 1/2 ab sin C in non-right-triangle problems.
Locate right triangles inside 3D solids before calculating lengths or angles.
Combine several geometry steps before giving a length or angle to the required accuracy.

[Maximum number: 4]

Figure for Question 9.B 2D and 3D trigonometry question 1 — Edexcel IGCSE Math B

Figure 3 shows a solid right prism ABCDEFGH.
Diagram NOT accurately drawn.
The base of the prism, ABCD, is a rectangle and is horizontal. Trapezium BCHG is a cross section of the prism.
$AB=4\text{ m},\quad BC=3\text{ m},\quad CH=2.4\text{ m},\quad GB=1.5\text{ m}$ $\angle GBC=\angle BCH=\angle ABG=\angle DCH=90^\circ$

The point P lies on the line GH such that $GP=\frac23GH$ .
The point Q lies on the line BC such that $BQ=\frac23BC$ .
Calculate, in degrees to one decimal place, $\angle APQ$ .

$PQ=1.5+\frac23(2.4-1.5)=2.1$ $AQ=\sqrt{4^{2}+2^{2}}=\sqrt{20}$ $\tan\angle APQ=\frac{\sqrt{20}}{2.1}$
Final answer:
$64.8^\circ$
Only allow $65^\circ$ from correct working.

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9.B 2D and 3D trigonometry question 1