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GEOMETRY 8.3 Trigonometry

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SIMILAR Triangles have the same RATIOS of SIDES

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GEOMETRY 8.3 Trigonometry

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IMPORTANT: Sine, Cosine, and Tangent of an Angle Are FRACTIONS!

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GEOMETRY 8.3 Trigonometry W A I T !!! How can we REMEMBER to Sine, Cosine & Tangent??? SOH CAH TOA

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Geometry 8.3One Way to Remember the RATIOS S Sine O Opposite over H Hypotenuse

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S Sine O Opposite over H Hypotenuse C Cosine A Adjacent over H Hypotenuse Geometry 8.3One Way to Remember the RATIOS

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S Sine O Opposite over H Hypotenuse C Cosine A Adjacent over H Hypotenuse T Tangent O Opposite over A Adjacent Geometry 8.3One Way to Remember the RATIOS

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SOHCAHTOA – I met him in Geometry Sine, Cosine and Tangent – He can Calculate ALL three (Equations) Thank you SOHCAHTOA I’m Really Glad to Know Ya You’re the CHIEF of Trigonometry

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GEOMETRY 8.3 Trigonometry

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If SIMILAR Triangles have CONGRUENT Corresponding Angles THEN Then Angles with the SAME Measures Must have the SAME SINE, COSINE and COSINE Ratios RATIOS are Usually Shown as 4 digit DECIMALS

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GEOMETRY 8.3 Trigonometry Historically, the Ratios related with particular angles were shown in Tables NOW, you can find out the ratio for a particular angle measure using your Calculator. Make SURE your Calculator MODE is in DEGREES !!!

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GEOMETRY 8.3 Trigonometry 45 What is :

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GEOMETRY 8.3 Trigonometry

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SINE Inverse (also called ARCSINE) reverses the SIN equation: GEOMETRY 8.3 Trigonometry Sine, Cosine and Tangent find SIDES Sin -1, Cos -1 Tan -1 find ANGLE Measures

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Use your Calculator to determine SIN -1 by: Press 2 nd, then SIN Enter the Ratio Press ENTER to get degrees of the Angle. SINE Inverse (also called ARCSINE) reverses the SIN equation: GEOMETRY 8.3 Trigonometry

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Use your Calculator to determine Angle A: If Side a = 5, and Hypotenuse c = 8 If Side a = 10, and Hypotenuse c = 40 If Side a = 15, and Hypotenuse c = 18 Use your Calculator to determine SIN -1 by: Press 2 nd, then SIN Enter the Ratio Press ENTER to get degrees of the Angle. GEOMETRY 8.3 Trigonometry

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Geometry 8.3 Using the SIN and SIN -1 Equations Geometry 8.3 Using the SIN and SIN -1 Equations A B C a b c If Side a = 8 and Side c = 12 What is Angle A?

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Geometry 8.3 Using the SIN and SIN -1 Equations Geometry 8.3 Using the SIN and SIN -1 Equations Geometry 8.3 Using the SIN and SIN -1 Equations A B C a b c If Side c = 14 and Side a = 9 What is Angle A?

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Geometry 8.3 Using the SIN and SIN -1 Equations Geometry 8.3 Using the SIN and SIN -1 Equations Geometry 8.3 Using the SIN and SIN -1 Equations Geometry 8.3 Using the SIN and SIN -1 Equations A B C a b c If Side c = 22 and Side a = 6 What is Angle B?

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Geometry 8.3 Using the SIN and SIN -1 Equations A B C a b c If Angle A = 25, and Side c = 7 What is Side a?

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Geometry 8.3 Using the SIN and SIN -1 Equations A B C a b c If Angle A = 42, and Side a = 25 What is Side c?

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Geometry 8.3 Using the SIN and SIN -1 Equations A B C a b c If Angle B = 33, and Side c = 15 What is Side b?

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Geometry 8.3 What is the COSINE of 30 degrees 45 degrees 60 degrees What is the SINE of: COSINE is Equal to the SINE of the Angle’s Complement!

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Geometry 8.3 40 28 What is side b?

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Geometry 8.3 15 32 What is side c?

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Geometry 8.3 What is side b? 15 32 What is side c?

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Geometry 8.3 15 32 What is Side b?

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Geometry 8.3 36 43 ?

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Geometry 8.3 75 ? 25

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Geometry 8.3 ? 7 5

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14 15 ?

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Geometry 8.3 9 13 ?

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Geometry 8.3 17 33 ?

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Geometry 8.3 55 16 ? ?

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Geometry 8.3 10 ---------------- 14 ---------------- What is Angle ADB?

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Geometry 8.3

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A water slide is a straight ramp 25 meters long that starts from the TOP of a tower 21 meters tall. Find the ANGLE the slide forms with the Tower.

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Geometry 8.3 According to the Americans with Disabilities Act, a ramp can RISE no more than 1 foot for every 12 feet of HORIZONTAL distance. What is the MAXIMUM angle that the ramp can form with the ground?

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Geometry 8.3 The Grade of the Pike’s Peak cog railway is 18 percent. That is, for every 100 feet of horizontal run, the train RISES 18 feet. Find the angle of the inclination of the railway.

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GEOMETRY 8.3 Trigonometry

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