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Trigonometry: SIN COS TAN or

Trigonometry: SIN COS TAN or. SOHCAHTOA. We will use Trigonometry to solve a number of problems. How could you find the height of this flagpole?. Measure the length of the shadow, and the angle of elevation. x. SOHCAHTOA. First identify the sides of the triangle. SOHCAHTOA.

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Trigonometry: SIN COS TAN or

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  1. Trigonometry:SIN COS TANor SOHCAHTOA

  2. We will use Trigonometry to solve a number of problems How could you find the height of this flagpole? Measure the length of the shadow, and the angle of elevation x SOHCAHTOA

  3. First identify the sides of the triangle SOHCAHTOA The longest side is called the… Hypotenuse. The side opposite is called the… Opposite. The remaining side is the… Adjacent HYP OPP x ADJ

  4. The Calculations SOHCAHTOA Suppose you measure the length of shadow to be 12 metres. This is “ADJ” Suppose the angle is 40 OPP Which trig button is this? Hint: TOA Tan x  ADJ OPP = Tan 40  12 = 0.839  12 = 10.07 m OPP 40 ADJ = 12

  5. Another example SOHCAHTOA Joe buys a ladder which extends to 5 metres. However he would not feel safe if the angle of the ladder exceeds 70 5 How far up the wall would the ladder extend at this angle? What trig function is needed? Hint:You know the HYP OPP 70 You need SIN

  6. The Calculation SOHCAHTOA The length of ladder is 5 m; this is “HYP” OPP Which trig button is this? Hint: SOH Sin x  HYP OPP = Sin 70  HYP OPP = Sin 70  5 = 0.940  5 = 4.70 m OPP 5 70

  7. Finding an Angle SOHCAHTOA The base of this triangle is 4 cms, the hypotenuse is 5 cms. How can you find the angle x? Which trig button is this? Hint: _AH HYP = 5 OPP Use COS…..BUT x Cos x = ADJ  HYP Cos x = 4  5 = 0.8 In order to find the angle, use ”SHIFT COS” (or INV COS) ADJ = 4 ADJ Cos x  HYP x = COS-1 0.8 =36.9

  8. Another example SOHCAHTOA Sue has a ladder which reaches 3m up the wall when the angle is 59 How long is the ladder? HYP OPP 59 What trig function is needed? Hint:You know OPP You need SIN OPP HYP = OPP  Sin 59 = 3  0.8572 = 3.5 m Sin x  HYP

  9. A further example SOHCAHTOA A stepladder has the shape of an isosceles triangle. The distance between its feet is 2.2 m. The angle the legs make with the horizontal is 64 64 2.2 m • How long are the sides of the ladder? • How high does the top reach?

  10. SOHCAHTOA Calculations First you need to work with a right angled triangle. C AC is the hypotenuse in ABC. AB is the adjacent, length 1.1 m. HYP OPP What trig button is needed? 64 A D B You need COS ADJ = 1 .1 HYP AC = AB  cos 64 = 1.1 0.438 = 2.5 m ADJ Cos x  How do you find the height BC? HYP

  11. Finding the Height SOHCAHTOA You could use TAN. OPP OPP Tan x  ADJ OPP = Tan 64  ADJ = 2.050  1.1 = 2.26 m. ADJ = 1 . 1

  12. A Final example SOHCAHTOA The participants in a TV series are ‘dumped’ on an uninhabited island somewhere… One of the problems they have to solve is to find the location of their island. The first step is to find the latitude - essentially, this determines how far north (or south) you are. This can be done by measuring the angle the North Star makes with the horizontal. (At the North Pole, it is overhead!) It would be quite feasible to make a rudimentary protractor, but this might not be very accurate. SO...

  13. The Solution SOHCAHTOA The idea is to line up the star with a suitable tall object, whose height you can measure. To keep things simple, let’s suppose you have a 4m pole. Also suppose that when you line up your eye, the North Star appears behind the top of the pole, and your eye is 432 cms from the pole as measured along the horizontal. What sides in the triangle do you know? 400 cms The Opposite and Adjacent. 432 cms Which Trig. Button is this?

  14. The Latitude SOHCAHTOA OPP Use Tan Tan x  ADJ Tan x = 400  432 = 0.9259 To find the angle x, you must do “Shift Tan” (or Tan-1) Tan-1 0.9259 = 42.8. (Your latitude is 42.8)

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