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Finding the Missing Side

Finding the Missing Side. Year 11. Here’s the problem. An anchor cable shelves at 50 º. You are aware that 24m of cable has been let out. What is the depth of water?. 50 º. 1. Draw diagram. x. 24m. 2. Label inside. With. 50 º. H , O & A. x. 24m. 50 º. x. 24m. A. O. H. 3.

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Finding the Missing Side

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  1. Finding the Missing Side Year 11

  2. Here’s the problem • An anchor cable shelves at 50º. You are aware that 24m of cable has been let out. What is the depth of water?

  3. 50º 1. Draw diagram x 24m

  4. 2. Label inside With 50º H, O & A x 24m

  5. 50º x 24m A O H

  6. 3. Select ratio A 50º O H x 24m

  7. SOHCAHTOA If given the opposite and the hypotenuse, use: sin = opposite hypotenuse If given the adjacent and the hypotenuse, use: cos = adjacent hypotenuse If given the opposite and the adjacent, use: tan = opposite adjacent

  8. 50º O Sin θ = H A As there is nothing on the Adjacent side, we use O x H must 24m Sine

  9. O A Sin θ = H 50º O H x 24m Substitute values 4.

  10. O A Sin θ = H 50º x O Sin 50º = H x 24 24m

  11. O Sin θ = H A 50º x Sin 50º = 24 O H x 24m 5. Rearrange We need to get x = ……

  12. A A B = 2 = C 5 Algebra revision If B = 2 and C = 5, find O Multiply both sides by 5 X 5 X 5 10 = A

  13. O Sin θ = H A 50º O H x 24m x Sin 50º = 24

  14. O Sin θ = x H ( x 24) Sin 50º = (24 x) A 24 50º O H x 24m

  15. O Sin θ = x H ( x 24) Sin 50º = (24 x) A 24 50º O H x 24m

  16. O Sin θ = H x Sin 50º = 50º 24 x = 24xSin 50º x 24m A O H

  17. O Sin θ = H 50º x Sin 50º = O x 24 24m x = 24xSin 50º Now use calculator and round off 6. Use Calculator A H

  18. O Sin θ = A H 50º x Sin 50º = O H x 24 24m x = 24xSin 50º x = 18.39m

  19. 50º Therefore… The depth of water is 18.39m x 24m

  20. The six steps are:- 1. Draw diagram 2. Label inside 3. Select ratio 4. Substitute values 5. Rearrange 6. Use Calculator

  21. An example • Ex 7B 1e 1. Draw diagram 2. Label inside 3. Select ratio 4. Substitute values 5. Rearrange 6. Use Calculator

  22. Your Turn Page 251 Ex 7B Qu1 a, d, f, g, h, i

  23. A real problem • UHF Communication is a radio system that works on line of sight. Why did the ships helicopter lose communication when only at an altitude of XXm and range of XXm • Colombus could work it out!!

  24. Solution • I

  25. Finding the length of the Hypotenuse

  26. Watch out 40cm 75º y Some problems are tricky

  27. A B = C Algebra Revision If B = 3 and A = 12, find C 12 3 = Multiply both sides by C X C C 3C = 12 Divide both sides by 3 3 3 Note how the C and 3 have swapped places C = 4

  28. A Cos θ = 40cm H A 75º O H y

  29. A Cos θ = 40cm H A 75º O H y

  30. A Cos θ = 40cm H A 75º 40 Cos 75º = y O H y

  31. A Cos θ = 40cm H A 75º O H y 40 Cos 75º = y

  32. A Cos θ = 40cm H A 75º 40 ( x y ) Cos 75º = ( yx ) y O H y

  33. A Cos θ = 40cm H A 75º 40 ( x y ) Cos 75º = ( yx ) y O H y

  34. A Cos θ = 40cm H A 75º 40 Cos 75º = y O y x Cos 75º = 40 H y

  35. A Cos θ = 40cm H A 75º 40 Cos 75º = y O y x Cos 75º = 40 H y

  36. A Cos θ = 40cm H A 75º 40 Cos 75º = y O y x Cos 75º = 40 H y Cos 75º Cos 75º

  37. A Cos θ = 40cm H A 75º 40 Cos 75º = y O y x Cos 75º = 40 H y Cos 75º Cos 75º

  38. A Cos θ = 40cm H A 75º 40 Cos 75º = y 40 O H y = y Cos 75º

  39. A Cos θ = 40cm H A 75º 40 Cos 75º = y 40 O H y = y Cos 75º y = 154.55 cm

  40. An example • 7B 2e

  41. Your turn Page 251 Ex 7B Qu2 a, c, d, f, i, l Qu3 do any five

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