Mathematical Methods — Question 16

ANSWER

$163$ m

Worked solution

Using the bearings gives an included ground angle of $110^\circ$. The horizontal distances to the tower satisfy $$\tan28^\circ=\frac{60}{b},\qquad \tan35^\circ=\frac{60}{a},$$ so $b=112.84$ m and $a=85.69$ m. Then by the cosine rule, $$c^2=85.69^2+112.84^2-2(85.69)(112.84)\cos110^\circ,$$ giving $c=163.37$ m. The distance between A and B is 163 m.

correctly establishes the angles using given bearings

[1 mark]

correctly determines the distance a and b

[1 mark]

determines distance between A and B

[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.