1 / 23

Right Angled Trigonometry

Right Angled Trigonometry. Labeling a Right Triangle. In trigonometry, we give each side a name according to its position in relation to any given angle in the triangle: Hypotenuse, Opposite, Adjacent. The _________ is always the longest side of the triangle. hypotenuse. Hypotenuse.

sebastian-mathis
Download Presentation

Right Angled Trigonometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Right Angled Trigonometry

  2. Labeling a Right Triangle • In trigonometry, we give each side a name according to its position in relation to any given angle in the triangle: Hypotenuse, Opposite, Adjacent • The _________ is always the longest side of the triangle. hypotenuse Hypotenuse Adjacent • The _________ side is the leg directly across from the angle. opposite  Opposite • The _________ side is the leg alongside the angle. adjacent

  3. Trigonometric Ratios We define the 3 trigonometric ratios in terms of fractions of sides of right angled triangles.  Hypotenuse (HYP) Adjacent (ADJ) Opposite (OPP)

  4. SohCahToa Sine equals Opposite over Hypotenuse Cosine equals Adjacent over Hypotenuse Tangent equals Opposite over Adjacent

  5. Practice Together: a 32 x Given each triangle, write the ratio that could be used to find x by connecting the angle and sides given. b x 65

  6. YOU DO: d c x Given the triangle, write all the ratios that could be used to find x by connecting the angle and sides given. 56

  7. In a right triangle, 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 finding the missing sides of a right triangle using trigonometric ratios: • Redraw the figure and mark on it HYP, OPP, ADJ relative to the given angle 9.6 cm HYP x ADJ 61 OPP

  9. Steps to finding the missing sides of a right triangle using trigonometric ratios: • For the given angle choose the correct trigonometric ratio which can be used to set up an equation • Set up the equation 9.6 cm HYP x ADJ 61 OPP

  10. Steps to finding the missing sides of a right triangle using trigonometric ratios: • Solve the equation to find the unknown. 9.6 cm HYP x ADJ 61 OPP

  11. Practice Together: x m Find, to 2 decimal places, the unknown length in the triangle. 7.8 m 41

  12. a m YOU DO: b m 63 14.6 m Find, to 1 decimal place, all the unknown angles and sides in the triangle. 

  13. Steps to finding the missing angle of a right triangle using trigonometric ratios: • Redraw the figure and mark on it HYP, OPP, ADJ relative to the unknown angle 5.92 km OPP ADJ 2.67 km HYP 

  14. Steps to finding the missing angle of a right triangle using trigonometric ratios: • For the unknown angle choose the correct trig ratio which can be used to set up an equation • Set up the equation 5.92 km OPP ADJ 2.67 km HYP 

  15. Steps to finding the missing angle of a right triangle using trigonometric ratios: • Solve the equation to find the unknown using the inverse of trigonometric ratio. 5.92 km OPP ADJ 2.67 km HYP 

  16. Practice Together: 3.1 km Find, to one decimal place, the unknown angle in the triangle. 2.1 km 

  17. YOU DO: 7 m 4 m Find, to 1 decimal place, the unknown angle in the given triangle. 

  18. Practice: Isosceles Triangles • Using what we already know about right angles in isosceles triangles find the unknown side. x cm 67 10 cm

  19. YOU DO: Isosceles Triangles • Find the unknown angle of the isosceles triangle using what you already know about right angles in isosceles triangles. 5.2 m 8.3 m 

  20. Practice: Circle Problems • Use what you already know about right angles in circle problems to find the unknown angle. 10 cm 6 cm 

  21. YOU DO: Circle Problems • 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: x cm 10 cm 65 48

  23. YOU DO: Other Figures (Rhombus) • A rhombus has diagonals of length 10 cm and 6 cm respectively. Find the smaller angle of the rhombus.  6 cm 10 cm

More Related