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Warmup: What is wrong with this? 30 ⁰

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8.3 and 8.4 Trigonometric Ratios

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Finding Trig Ratios A trig ratio is a ratio of the lengths of two sides of a right triangle. The word trigonometry is derived from the ancient Greek language and means measurement of triangles. The three basic trig ratios are sine, cosine, and tangent. Abbreviated as sin, cos, and tan respectively

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Trigonometric Ratios Let ∆ABC be a right triangle. If you are standing from angle A, the following sides are labeled: opposite, adjacent and hypotenuse sin A = opposite hypotenuse = a c cos A = adjacent hypotenuse = b c tan A = opposite adjacent = a b

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Trigonometric Ratios If you were standing at angle B, you would have to re- label the sides of opposite, adjacent and hypotenuse sin B = opposite hypotenuse = b c cos B = adjacent hypotenuse = a c Tan B = opposite adjacent = b a a c b side opposite to angle B Side adjacent angle B hypotenuse A B C

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The famous Indian… SOHCAHTOA

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Ex. 1: Find sin, cos and tan of angle S Ratio SS sin S = opposite hypotenuse cosS = adjacent hypotenuse tanS = opposite adjacent 12 13 5 R TS

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Ex.2: Find the sin, cos and tan of angle R Ratio RR sin R = opposite hypotenuse cosR= adjacent hypotenuse tanR = opposite adjacent 12 13 5 R TS

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Using the Inverse You can use the sin, cos and tan ratio and calculate it’s inverse, sin -1, cos -1, tan -1 to find the measure of the angle. Make sure your calculator is in degree mode!!! *make note: sin, cos, and tan are ratios. Inverses find angles!!!

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Let’s find angle S. Ratio SS sin S = opposite hypotenuse cosS = adjacent hypotenuse tanS = opposite adjacent 12 13 5 R TS

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Now let’s find the angle measure from a previous example Ratio RR sin R = opposite hypotenuse cosR= adjacent hypotenuse tanR = opposite adjacent 12 13 5 R TS

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Examples: Given the triangles below, find the missing angle measure to the nearest degree 2 6 ? 6 8 10 ?

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Practice: Solve for the missing variables 1.)2.) 3.)4.) x⁰x⁰ 12 16 7 26 ⁰ m 40 ⁰ 9 y z 30 15 (No decimal answers in 4) p

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