IB Maths AA SL 3.2 Triangle trigonometry Question Bank

Practise IB Mathematics SL/HL 3.2 by applying triangle trigonometry methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 3]

All lengths in this question are in centimetres.
A solid metal ornament is in the shape of a right pyramid, with vertex V and square base ABCD . The centre of the base is X . Point V has coordinates (1,5,0) and point A has coordinates (-1,1,6).

Figure for Question SL 3.2—Triangle trigonometry question 1 — IB Maths AA SL

Given that $\mathrm{A} \hat{\mathrm{V}} \mathrm{B}=40^{\circ}$ , find AB .

The volume of the pyramid is $57.2 \mathrm{~cm}^{3}$ , correct to three significant figures.

(b) METHOD 1 attempt to apply cosine rule OR sine rule to find AB
$(\mathrm{AB}=) \sqrt{7.48 \ldots^{2}+7.48 \ldots^{2}-2 \times 7.48 \ldots \times 7.48 \ldots \cos \left(40^{\circ}\right)}$ OR $\frac{\mathrm{AB}}{\sin 40^{\circ}}=\frac{\sqrt{56}}{\sin 70^{\circ}}$ $=5.11888 \ldots$ $=5.12(\mathrm{~cm})$
METHOD 2
Let M be the midpoint of $[\mathrm{AB}]$
attempt to apply right-angled trigonometry on triangle AVM
$=2 \times 7.48 \ldots \times \sin \left(20^{\circ}\right)$ $=5.11888 \ldots$ $=5.12(\mathrm{~cm})$

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SL 3.2—Triangle trigonometry question 1