IB Maths AA SL 3.2 Triangle Trigonometry Questions

Practise choosing right-triangle, sine-rule, cosine-rule or area methods, combining them with bearings or Pythagoras and checking units and ambiguity.

Exam points

Use sine, cosine or tangent in a right-angled triangle to determine a missing side or angle from a labelled diagram.
Apply the sine rule or cosine rule to find unknown sides and angles in a non-right triangle, selecting the correct opposite side/angle pairing.
Use the area formula 1/2 ab sin C to calculate or optimise a triangular area, including when the included angle is known or constrained.
Combine triangle-trigonometry results with Pythagoras, bearings, chords or a geometric model, checking units, angle mode and any stated ambiguity.

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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 IB Maths AA SL 3.2 Triangle Trigonometry Questions 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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IB Maths AA SL 3.2 Triangle Trigonometry Questions question 1