#Measurement #Year12 #Standard >[!info]- [Trigonometry | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-standard-11-12-2024/content/n12-tba2/fa6dd765ae) >- MST-12-S2-04 applies trigonometry to solve problems involving right-angled and non-right-angled triangles ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | -------------------------- | -------------------------------------------- | ------------------------------- | | [[Right-angled Triangles]] | - Pythagoras' theorem | - solving trigonometry problems | | [[Trigonometry A]] | - trig ratios | - *repeated content* | | [[Trigonometry B]] | - angle of elevation/depression, bearings | - *repeated content* | | [[Trigonometry C]] | - sine rule, cosine rule, sine rule for area | - *repeated content* | ## Trigonometry - Apply trigonometric ratios to right-angled triangles to find either the lengths of unknown sides or the size of unknown angles in both degrees, and degrees and minutes - Apply the sine rule $\frac{a}{\sin{A}}=\frac{b}{\sin{B}\ }=\frac{c}{\sin{C}}$ in a given triangle $ABC$ to find the value of an unknown side - Apply the sine rule $\frac{\sin{A}}{a}=\frac{\sin{B}}{\ b}=\frac{\sin{C}}{c}$ in a given triangle $ABC$ to find the value of an unknown angle, excluding the ambiguous case - Apply the sine rule in a given triangle to find the value of an unknown angle, given that the unknown angle is obtuse - Apply the cosine rule $c^2=a^2+b^2-2ab\cos{C}$ in a given triangle $ABC$ to find the value of an unknown side - Apply the cosine rule $\cos{C}=\frac{a^2\ +\ b^{2\ }-\ c^2}{2ab}$ in a given triangle ABC to find the value of an unknown angle - Apply the formula $A=\frac{1}{2}ab\sin{C}$, where $a$ and $b$ are the sides that form the included angle $C$ in a given triangle $ABC$, to solve problems in a range of contexts - Identify and interpret true bearings and compass bearings and convert between them - Construct and interpret compass radial surveys and solve related problems - Solve practical problems involving Pythagoras’ theorem, the trigonometry of right-angled and non-right-angled triangles, angles of elevation and depression, and true bearings and compass bearings