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Find the missing edges (correct to 1 decimal place)

Find the missing edges (correct to 1 decimal place). a. 6cm. b. 5cm. 4cm. 9cm. 16cm. 11cm. d. 1cm. 1cm. c. Answers. 7.2cm. 6cm. 10.3cm. 5cm. 4cm. 9cm. 16cm. 11cm. 1.4cm. 1cm. 1cm. 11.6cm. We can label the sides of a right-angled triangle in the following way:.

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Find the missing edges (correct to 1 decimal place)

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  1. Find the missing edges(correct to 1 decimal place) a 6cm b 5cm 4cm 9cm 16cm 11cm d 1cm 1cm c

  2. Answers 7.2cm 6cm 10.3cm 5cm 4cm 9cm 16cm 11cm 1.4cm 1cm 1cm 11.6cm

  3. We can label the sides of a right-angled triangle in the following way: Hypotenuse (H) This is the longest side and is opposite the right-angle Opposite Side (O) This is the side opposite the angle in question Adjacent Side (A) This is the side adjacent (next to) the angle in question.

  4. Label the sides of the right-angled triangles on the sheet.

  5. dustonschoolmaths does trigonometry… http://www.youtube.com/watch?v=XyCdqyPFP50

  6. Calculate the length of side p. A Hyp C H p 46° p = adj ÷ cos θ p = 7 ÷ cos 46 7cm p = 10.08 cm Adj

  7. Calculate the size of angle Q. O T A 4.3m Opp tan Q = opp ÷ adj Q° tan Q = 4.3 ÷ 3.8 3.8m Q = tan-1 (4.3 ÷ 3.8) Adj Q = 49°

  8. Answers 1. a = 12.03 cm b = 61.44 cm c = 41.80 cm d = 115.19 cm 2. a = 69.5° b = 33.5° c = 69.4° d = 54.4° 3. 2.25 m 4. 48.2o 5. 9.21 m Extension: 12.073 cm (3dp)

  9. Show me and example of: • A hypotenuse • An opposite side • An adjacent side • A problem that can be solved using trigonometry • A triangle in which the tangent of the angle is 1 • A triangle in which the cosine is 0.5

  10. What is the same/different about three triangles with sides 3, 4, 5 and 6, 8, 10 and 5, 12, 13 True/Never/Sometimes: - You can use trigonometry to find the missing length/angle in triangles

  11. The image below is of a cuboid. Calculate the size of the angle between CE and EFGH. C EG² = EH² + HG² = 4² + 3² = 25 EG = √25 = 5 cm B C D A 11cm 11cm G F 3cm E E G H ? cm 4cm

  12. The image below is of a cuboid. Calculate the size of the angle between CE and EFGH. C B C O D A T A 11cm tan = opp ÷ adj 11cm Opp tan = 11 ÷ 5 G F = tan-1 (11 ÷ 5) 3cm = 66° E E G H 5 cm 4cm Adj

  13. Answers 1. 10.2° 2. a. 9.11 cm b. 19.2°

  14. Starter Find the lengths of the missing sides. Give your answer in surd form where appropriate. 14 cm 2√33 _____ cm 4 cm 6 ___ cm 8 cm 5 cm 4√5 ____ cm 4 cm 16 cm

  15. Make sure you fill in your table as we go – you’ll need it later!

  16. Periodic… Symmetrical…

  17. Periodic… Symmetrical…

  18. Periodic…

  19. Remember: (You may want to copy these down!) O A O H H A sin cos tan

  20. Let’s start with an isosceles right-angled triangle with equal sides of 1 cm. These angles are equal and angles in a triangle sum to 180°. 45° 1 cm 45° 1 cm

  21. Let’s start with an isosceles right-angled triangle with equal sides of 1 cm. 45° √2 cm 1 cm By Pythagoras’ Theorem, the hypotenuse is √2. 45° 1 cm

  22. sin 45° = _1_ √2 45° √2 cm 1 cm 45° 1 cm

  23. sin 45° = _1_ √2 45° cos 45° = _1_ √2 √2 cm 1 cm 45° 1 cm

  24. sin 45° = _1_ √2 45° cos 45° = _1_ √2 √2 cm 1 cm tan 45° = 1 = 1 1 45° 1 cm

  25. sin 45° = √2 2 sin 45° = _1_ √2 45° cos 45° = √2 2 cos 45° = _1_ √2 √2 cm 1 cm tan 45° = 1 = 1 1 45° 1 cm Rationalising the denominators gives…

  26. Now let’s look at an equilateral triangle with sides of 2 cm. 60° 2 cm 2 cm 60° 60° 2 cm

  27. By Pythagoras’ Theorem, the height is √3. Now let’s look at an equilateral triangle with sides of 2 cm. 30° 2 cm √3 cm 60° 1 cm

  28. sin 30° = 1 2 30° 2 cm √3 cm 60° 1 cm

  29. sin 30° = 1 2 30° cos 30° = √3 2 2 cm √3 cm 60° 1 cm

  30. sin 30° = 1 2 30° cos 30° = √3 2 2 cm √3 cm tan 30° = _1_ √3 60° 1 cm

  31. Rationalising the denominator gives… sin 30° = 1 2 30° cos 30° = √3 2 2 cm √3 cm tan 30° = √3 3 tan 30° = _1_ √3 60° 1 cm

  32. sin 60° = √3 2 30° 2 cm √3 cm 60° 1 cm

  33. sin 60° = √3 2 30° cos 60° = 1 2 2 cm √3 cm 60° 1 cm

  34. sin 60° = √3 2 30° cos 60° = 1 2 2 cm √3 cm tan 60° = √3 1 60° 1 cm

  35. sin 60° = √3 2 30° cos 60° = 1 2 2 cm √3 cm tan 60° = √3 1 60° 1 cm

  36. Answers Question 1 a) ½ b) 1 c) ½ d) - ½ e) f) -1 Question 2 a) b) Question 3 Question 4 a) 12√3 m² b) 28 m Question 5 sin 270° sin 10° sin 135° sin 90°

  37. Trigonometry Help Flow Chart Is the triangle right-angled? Yes No Does the question involve any angles? Do you know a side and an opposite angle? Yes No No Yes Use the Cosine rule Use the Sine rule Use Pythagoras’ Theorem Use trig ratios SOHCAHTOA

  38. Show me and example of: • A problem that can be solved using the sine rule • A problem that can be solved using the cosine rule • A triangle which you can find the area of

  39. Group activity Put 3 triangles in each column to identify the method you would use to find the missing information. Make sure you can justify every triangle. Extension: How many can you solve?

  40. Answers

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