Standard Measurement - Non-right angled trigonometry

This lesson comprises four (4) master classes focusing on:

• Trigonometric ratios
• Pythagoras’ theorem
• Sine rule
• Cosine rule
• Compass and true bearing
• Radial surveys

Content:

MS-M6

• Review and use the trigonometric ratios to find the length of an unknown side or the size of an unknown angle in a right-angled triangle
• Use technology to investigate the sign of \( \sin A \) and \( \cos A \) for \( 0^{\circ} \le A \le 180^{ \circ } \)
• Determine the area of any triangle, given two sides and an included angle, by using the rule \( A=\frac{1}{2}ab \sin C \), and solve related practical problems
• Solve problems involving non-right-angled triangles using the sine rule, \( \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \) (ambiguous case excluded)
  • find the size of an obtuse angle, given that it is obtuse
• Solve problems involving non-right-angled triangles using the cosine rule, \( c2=a^2+b^2−2ab\cos C \)
• Understand various navigational methods
  • understand the difference between compass and true bearings
  • investigate navigational methods used by different cultures, including those of Aboriginal and Torres Strait Islander Peoples
• Solve practical problems involving Pythagoras’ theorem, the trigonometry of right-angled and non-right angled triangles, angles of elevation and depression and the use of true bearings and compass bearings
  • work with angles correct to the nearest degree and/or minute
• Construct and interpret compass radial surveys and solve related problems