Mathematical Methods — Question 15

ANSWER

a) See official solution diagram; b) $4\sqrt3\text{ cm}^2$

Worked solution

a) The official sample response labels the isosceles triangle with $a=4$, $b=4$ and $C=120^\circ$.

b) $$\text{Area}=\frac12(4)(4)\sin120^\circ=\frac12(4)(4)\frac{\sqrt3}{2}=4\sqrt3\text{ cm}^2.$$

correctly labels the given angle and sides in the isosceles triangle

[1 mark]

establishes expression for the area

[1 mark]

correctly determines the exact value of sine

[1 mark]

determines area in simplest form

[1 mark]

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