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The Tangent Ratio
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The Tangent Ratio

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The Tangent Ratio in Trigonometry and Triangles Mathematics

The Tangent Ratio in Trigonometry and Triangles Mathematics

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  • 1. Image Source: Jeff Wilson Photography
  • 2. After take-off, a plane ascends at a specific Angle of Elevation so that it can fly a certain distance, and attain a certain height, to thereby reach the cruising altitude for its assigned flight path. Opposite and Adjacent of a Right Triangle are involved with this angle in a relationship called a “Tangent” Ratio.
  • 3. Opposite Adjacent ɵo Adjacent - ADJ - A Opposite-OPP-O ɵTangent = OPP ADJ ɵTangent = O / AɵTan = The “Tangent” Ratio for a Right Triangle is defined as the Opposite Side Length divided by the Adjacent Length. If we have several right triangles with the same Reference Angle, the ratio of their Opposite divided by the Adjacent will be the same value for all of these Triangles.
  • 4. Eg. If we look at the Opposite / Adjacent for each of the above three Triangles we get Tan37o = 3 / 4 = 6 / 8 = 9 / 12 = 0.75 37 o 37 o 37 o 3 4 6 8 9 12 The Tangent Ratio of Opposite / Adjacent is the same value.
  • 5. ɵo OPP ADJ ɵTan = These are the four formulas for working with Tangent Triangles. OPP = ADJ x Tanɵ ɵ = Tan-1 OPP Tanɵ OPP ADJ ADJ = We also use the special “Tan” and “Tan-1 ” calculator buttons when solving Tangent Triangles. Adjacent - ADJ - A Opposite-OPP-O
  • 6. We use the special “Tan” and “Tan-1 ” calculator buttons when solving Tangent Triangle Questions. Warning: Your calculator must be in “Degrees” DEG Mode. Tan 60o tan 60 enter 1.7321 Tan 45o tan 45 enter 1 Tan 30o tan 30 enter 0.5774 Note that we round off long decimal trig values from the calculator to four decimal places.
  • 7. To get “Tan-1 ” on the calculator we use “2nd” or “Fn” followed by the “Tan” calculator button. Warning: Your calculator must be in “Degrees” DEG Mode. 60o tan 1.7321 enterTan-1 (1.7321) Note that we usually round off angle values from the calculator to the nearest whole number 2nd 35o tan 0.7071 enterTan-1 (0.7071) 2nd 37o tan 3 enterTan-1 (3/4) 2nd n/d 4
  • 8. 1. Label the Sides of the Triangle 2. Work out if unknown is OPP, ADJ, or the Angle. 3a. To find Unknown OPP, use O = A x Tanɵ 3b. To find an Unknown ADJ, use A = O / Tanɵ 3c. To find an Unknown Angle, use ɵ = Tan-1 (O / A ) 4. Substitute values into the formula being used 5. Put values into a Calculator and Round Off Answer
  • 9. To find Unknown OPP, use O = A x Tanɵ O = 10 x Tan35 O = 7.002 O = 7.00 m = 7 o m 10 35 o OPP m ADJ 10 35
  • 10. To find Unknown Angle, use β = Tan-1 (5 / 12) β = 22.6198 β = 23o 5 β ɵ = Tan-1 (OPP / ADJ) β
  • 11. http://passyworldofmathematics.com/ All slides are exclusive Copyright of Passy’s World of Mathematics Visit our site for Free Mathematics PowerPoints