IB Maths AI HL 3.2 Triangle trigonometry and inverse problems

[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.

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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 $\mathrm{AD}=89.2 \mathrm{~m}, \mathrm{DF}=104.9 \mathrm{~m}$ and $\mathrm{A} \hat{\mathrm{DF}}=83^{\circ}$ .

(a)

Find AF .

[ 3 ]

$\quad \mathrm{AF}^{2}=89.2^{2}+104.9^{2}-2(89.2)(104.9) \cos 83$
(M1)(A1)
Note: Award (M1) for substitution into the cosine rule and (A1) for correct substitution.

\mathrm{AF}=129 \mathrm{~m} \quad(129.150 \ldots)

(b)

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

Find the cost per metre of installing this cable.

[ 2 ]

$21310 \div 129.150 \ldots$
$ 165

IB Maths AI HL Sl 3 2 Triangle Trigonometry Questions question 1

Question (a)

Question (b)