IB Maths AI HL AI 3.1 practice question

Question 1

Paper 1Medium6 marks

A surveyor uses triangulation to estimate the area of a triangular wetland $ABC$ Points $A$ and $B$ lie on an accessible straight bank, and $AB=d$ metres. The measured interior angles are $\angle BAC=48^\circ$ and $\angle ABC=67^\circ$

(a)

Find $\angle ACB$

[1]

(b)

Show that the area $T$ in $\text{m}^2$ is approximately given by $T=0.377d^2$

[2]

(c)

The surveyor wants to map a region with an area of at least $6000\text{ m}^2$ Determine the required value of $d$ to 3 significant figures. Hence state whether a baseline of $125\text{ m}$ is sufficient.

[3]

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