IB Maths AA SL 3.3 Applications of Trigonometry

IB Mathematics: analysis and approaches guide, first assessment 2021

Practise translating bearings, elevation angles and real distances into labelled diagrams, then selecting triangle trigonometry to determine lengths, directions or times.

How this is tested

draw a labelled diagram from the context and mark bearings clockwise from north
select a trigonometric ratio, sine rule or cosine rule from the known sides and angles
interpret the calculated length, bearing or travel time with the required units and precision

[Maximum number: 1]

A boat sets off from a port P and travels on a bearing of $090^{\circ}$ until reaching point B .
A lighthouse L is 5 km from P on a bearing of $056^{\circ}$ .
The bearing of the lighthouse from B is $290^{\circ}$ .
This is shown in the following diagram.

Figure for Question 2(a) — IB Maths AA SL

Find the angle $\mathrm{L} \hat{\mathrm{PB}}$ .

How this is tested

Question 2(a)