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Right Angled Trigonometry Grade 9 Mathematics
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- 2. Labeling a RightTriangle In trigonometry, we give each side a name according to its position in relation to any given angle in the triangle: Hypotenuse, Opposite, Adjacent Hypotenuse Adjacent Opposite The _________ is always the longest side of the triangle. The _________ side is the leg directly across from the angle. The _________ side is the leg alongside the angle. hypotenuse opposite adjacent
- 3. Trigonometric Ratios We definethe 3 trigonometric ratios in terms of fractions of sides of right angled triangles. Hypotenuse (HYP) Adjacent (ADJ) Opposite (OPP)
- 4. SohCahToa Sine equals Oppositeover Hypotenuse Cosine equals Adjacent over Hypotenuse Tangent equals Opposite over Adjacent
- 5. Practice Together: Given eachtriangle, write the ratio that could be used to find x by connecting the angle and sides given. 65 a x 32 b x
- 6. YOU DO: Given thetriangle, write all the ratios that could be used to find x by connecting the angle and sides given. 56 d x c
- 7. In a righttriangle, if we are given another angle and a side we can find: The third angle of the right triangle: How? The other sides of the right triangle: How? Using the ‘angle sum of a triangle is 180’ Using the trigonometric ratios
- 8. Steps to findingthe missing sides of a right triangle using trigonometric ratios: 1. Redraw the figure and mark on it HYP, OPP, ADJ relative to the given angle 61 9.6 cm x HYP OPP ADJ
- 9. Steps to findingthe missing sides of a right triangle using trigonometric ratios: 2. For the given angle choose the correct trigonometric ratio which can be used to set up an equation 3. Set up the equation 61 9.6 cm x HYP OPP ADJ
- 10. Steps to findingthe missing sides of a right triangle using trigonometric ratios: 4.Solve the equation to find the unknown. 61 9.6 cm x HYP OPP ADJ
- 11. Practice Together: Find, to2 decimal places, the unknown length in the triangle. 41 x m 7.8 m
- 12. YOU DO: Find, to1 decimal place, all the unknown angles and sides in the triangle. a m 14.6 m 63 b m
- 13. Steps to findingthe missing angle of a right triangle using trigonometric ratios: 1. Redraw the figure and mark on it HYP, OPP, ADJ relative to the unknown angle 5.92 km HYP OPP ADJ 2.67 km
- 14. Steps to findingthe missing angle of a right triangle using trigonometric ratios: 2. For the unknown angle choose the correct trig ratio which can be used to set up an equation 3. Set up the equation 5.92 km HYP OPP ADJ 2.67 km
- 15. Steps to findingthe missing angle of a right triangle using trigonometric ratios: 4. Solve the equation to find the unknown using the inverse of trigonometric ratio. 5.92 km HYP OPP ADJ 2.67 km
- 16. Practice Together: Find, toone decimal place, the unknown angle in the triangle. 3.1 km 2.1 km
- 17. YOU DO: Find, to1 decimal place, the unknown angle in the given triangle. 7 m 4 m
- 18. Practice: Isosceles Triangles Using what we already know about right angles in isosceles triangles find the unknown side. 10 cm x cm 67
- 19. YOU DO: IsoscelesTriangles Find the unknown angle of the isosceles triangle using what you already know about right angles in isosceles triangles. 8.3 m 5.2 m
- 20. Practice: Circle Problems Use what you already know about right angles in circle problems to find the unknown angle. 6 cm 10 cm
- 21. YOU DO: CircleProblems Use what you already know about right angles in circle problems to find the unknown side length. 6.5 cm 56 x cm
- 22. Practice: Other Figures(Trapezoid) Find x given: 1 0 c m x c m 65 48
- 23. YOU DO: OtherFigures (Rhombus) A rhombus has diagonals of length 10 cm and 6 cm respectively. Find the smaller angle of the rhombus. 10 cm 6 c m