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TANGENT RATIO SPI 3108.4.15 SPI 3108.4.15 Determine and use the appropriate trigonometric ratio for a right triangle to solve a contextual problem Determine and use the appropriate trigonometric ratio for a right triangle to solve a contextual problem Jim Smith JCHS

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A B C HYPOTENUSE LEG

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TANGENT = OPPOSITE LEG ADJACENT LEG

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A B C HYPOTENUSE ADJACENT OPPOSITE Target Angle

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A BC 10 6 8 HYPOTENUSE Target Angle OPP ADJ

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TANGENT OPPOSITE LEG ADJACENT LEG A = 8 6 8 6 = 1.3333

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A BC 24 7 25 7 24 TAN A = HYP Target OPP ADJ O A 7 24 = 0.2917

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A BC 21 16 32 O A TAN C = 21 16 21 16 HYP Target OPP ADJ = 1.3125

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USING THE TANGENT RATIO X 6 55 0 OPP ADJ 3) X = 8.56 or 8.6 1) TAN 55 0 = X 6 1 2) 1.4281 = X 6

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2.7474 X 2.7474 70 0 18 x OPP ADJ 1) TAN 70 0 = 3) 4) X = 6.6 18 X 18 X 2.7474 = 2) 18 = 1 2.7474

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3 X 43 0 1)2) 18 0 X 27 3) 7X 39 0 4) 13 X 55 0

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1) TAN 43 = 3 / X.9325 = 3 / X.9325 X = 3 X = 3.2 2) TAN 18 = X / 27.3249 = X / 27 X = 8.8 3) TAN 39 = X / 7.8097 = X / 7 X = 5.7 4) TAN 55 = 13 / X 1.4281 = 13 / X 1.4281 X = 13 X = 9.1

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***REMEMBER*** SET CALCULATORS TO DEGREES SET CALCULATORS TO DEGREES SHOW ALL STEPS SHOW ALL STEPS TAN RATIOS TO 4 DECIMAL PLACES TAN RATIOS TO 4 DECIMAL PLACES ROUND ANSWERS TO 1 DECIMAL PLACE ROUND ANSWERS TO 1 DECIMAL PLACE

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