Quick questions on Area of a triangle using two sides and the included angle for HSC Maths Standard 2

The formula fails silently if you use an angle that is not between your two chosen sides, so it is worth being deliberate.

Before reaching for the cosine rule on an SSS triangle, glance at the three sides for a Pythagorean triple (three lengths where the two smaller ones squared add up to the largest one squared). Suppose $a^2 + b^2 = c^2$, for example $9$, $12$, $15$, which is $3$-$4$-$5$ scaled by $3$. Then the triangle is right-angled, and the right angle sits between the two shorter sides. Since $\sin 90\degree = 1$, the area is simply $\frac{1}{2} \times (\text{shorter side}) \times (\text{other shorter side})$.

Standard 2 works in degrees; check the mode before computing $\sin C$.

Area is in squared units (m$^2$, cm$^2$); a plain unit is a marking-guide error.