Mathematical Methods — Question 15

ANSWER

Bearing $263^\circ30'\text{ T}$.

Worked solution

From the bearing information, $\angle L=22^\circ$. Using the cosine rule, $$x^2=8^2+5.2^2-2(8)(5.2)\cos22^\circ,$$ so $x=3.7280$ km. Using the sine rule, $$\frac{3.7280}{\sin22^\circ}=\frac8{\sin C},$$ giving $C=53.5019^\circ$ or $126.4981^\circ$. The obtuse angle is required. Therefore the return bearing is $$360^\circ-126.4981^\circ+30^\circ=263^\circ30'\text{ T}.$$

correctly establishes the diagram using bearing and distance information

[1 mark]

correctly determines angle $L$

[1 mark]

determines unknown distance

[1 mark]

substitutes into appropriate rule

[1 mark]

determines obtuse angle at $C$

[1 mark]

determines direction needed to return to youth hostel using the obtuse angle for $C$

[1 mark]

shows logical organisation communicating key steps

[1 mark]

One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.