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IB Maths AI HL 3.2 Triangle trigonometry and inverse problems Question Bank

Practise IB Maths AI HL 3.2 by solving multi-step triangle problems involving bearings, elevation and applied measurement.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • Combine sine-rule or cosine-rule calculations to solve a chained triangle measurement problem.
  • Analyse an angle of elevation, bearing or cost model and preserve the correct geometric orientation.
  • Check for ambiguous or impossible solutions using the diagram, units and stated constraints.

SL 3.2—Triangle trigonometry question 1

[Maximum number: 5]

This question compares possible designs for a new computer network between multiple school buildings, and whether they meet specific requirements.
A school's administration team decides to install new fibre-optic internet cables underground. The school has eight buildings that need to be connected by these cables. A map of the school is shown below, with the internet access point of each building labelled A-H.

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

Jonas is planning where to install the underground cables. He begins by determining the distances, in metres, between the underground access points in each of the buildings.

He finds AD=89.2 m,DF=104.9 m\mathrm{AD}=89.2 \mathrm{~m}, \mathrm{DF}=104.9 \mathrm{~m} and ADF^=83∘\mathrm{A} \hat{\mathrm{DF}}=83^{\circ}.

Question (a)

(a)

Find AF .

The cost for installing the cable directly between A and F is $21310\$ 21310.

[ 3 ]

Question (b)

(b)

Find the cost per metre of installing this cable.

Jonas estimates that it will cost $110\$ 110 per metre to install the cables between all the other buildings.

[ 2 ]
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