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Trigonometry in Rightangled Triangles

Trigonometry in Rightangled Triangles. Module 8. Trigonometry. A method of calculating the length of a side Or size of an angle Calculator required. SINE Ratio – find Opposite side. Sine = Opposite Hypotenuse. C. Hypotenuse. 10.2cm. x. Opposite. Sine30 = x 10.2.

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Trigonometry in Rightangled Triangles

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  1. Trigonometry in Rightangled Triangles Module 8

  2. Trigonometry • A method of calculating the • length of a side • Or size of an angle • Calculator required

  3. SINE Ratio – find Opposite side Sine = Opposite Hypotenuse C Hypotenuse 10.2cm x Opposite Sine30 = x 10.2 30º B A x = 10.2 x Sine30 x = 5.1cm

  4. SINE Ratio – find Opposite side Sine = Opposite Hypotenuse C Hypotenuse 8.4cm x Opposite Sine46 = x 8.4 46º B A x = 8.4 x Sine46 x = 6.04245….cm x = 6.04cm (3 sig fig)

  5. SINE Ratio – find angle Sine = Opposite Hypotenuse C Hypotenuse Sin x = 3.4 9.1 9.1cm 3.4cm Opposite xº Sin-1 – Shift Sin B A Sin-1 (3.4÷9.1) = 21.939…º <ABC = 21.9º (3 sig fig)

  6. SINE Ratio – find Hypotenuse Sine = Opposite Hypotenuse C Hypotenuse Sin 32 = 3.2 x x cm 3.2cm Opposite 32º x = 3.2 Sin32 B A = 6.0386…cm BC = 6.04cm (3 sig fig)

  7. Cosine & Tangent? • Are TWO other ratios we can use • Similar process for calculating sides and angle • You now need to decide which ratio to use

  8. SOHCAHTOA Silly Sine = O H Sin Old Horace Caught Cosine = A H Cos A Haddock Trawling Tangent = O A Tan Off Afghanistan

  9. Ratios C Sin x = 3 5 5cm Hypotenuse 3cm Cos x = 4 5 Opposite xº B Tan x = 3 4 A 4cm Adjacent

  10. Which ratio to use? C Tan32 = x 3.2 Hypotenuse x cm Opposite x = 3.2 x Tan32 32º x = 1.9995….cm B A 3.2 cm Adjacent x = 2.00 cm (3 sig fig) ? √ ? √ SOH CAH TOA

  11. Which ratio to use? C Cos38 = 2.6 x Hypotenuse x cm Opposite x = 2.6 / Cos38 38º x = 3.299….cm B A 2.6 cm Adjacent x = 3.30 cm (3 sig fig) SOH CAH TOA

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