#MeasurementAndSpace #Path #Stn #Adv >[!info]- [Trigonometry C (Path) | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-5/fa381c0ce0) >- MA5-TRG-P-01 applies Pythagoras’ theorem and trigonometry to solve 3-dimensional problems and applies the sine, cosine and area rules to solve 2-dimensional problems, including bearings ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | --------------------------- | ----------------------------------------- | --------------------------------------------------------------------------------------- | | [[Right-angled Triangles]] | - Pythagoras' theorem | - 3D Pythagoras and trigonometry | | [[Equations B]] | - solving equations involving fractions | - sine and cosine rule | | [[Area and Surface Area B]] | - Slant heights | - 3D Pythagoras and trigonometry | | [[Trigonometry B]] | - Degrees, minutes, seconds<br>- Bearings | - rounding to nearest minute<br>- non-right-angled triangle problems involving bearings | ## [[Solve 3-dimensional problems involving right-angled triangles.pdf]] - Apply Pythagoras’ theorem to solve problems involving the lengths of the edges and diagonals of rectangular prisms and other 3-dimensional objects - Apply trigonometry to solve problems involving right-angled triangles in 3 dimensions, including using bearings and angles of elevation and depression ## [[Apply the sine, cosine and area rules to any triangle and solve related problems.pdf]] - Use graphing applications to verify the sine rule $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ and that the ratios of a side to the sine of the opposite angle is a constant - Apply the sine rule in a given triangle $ABC$ to find the value of an unknown side - Apply the sine rule in a given triangle $ABC$ to find the value of an unknown angle (ambiguous case excluded): $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ - Use graphing applications to verify the cosine rule $c^2=a^2+b^2-2ab\cos C$ - Apply the cosine rule to find the unknown sides for a given triangle $ABC$ - Rearrange the formula to deduce that $\cos C=\frac{a^2+b^2-c^2}{2ab}$ and use this to find an unknown angle - Use graphing applications to verify the area rule $A=\frac{1}{2}ab\sin{C}$. - Apply the formula $A=\frac{1}{2}ab\sin{C}$, where $a$ and $b$ are the sides that form angle $C$ to find the area of a given triangle $ABC$ - Solve problems involving finding unknown angles or sides in triangles (excluding right-angled triangles) by selecting and applying the appropriate rule