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Warmup: What is wrong with this? 30⁰ 8.3 and 8.4 Trigonometric Ratios 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 Trigonometric Ratios • Let ∆ABC be a right triangle. If you are standing from angle A, the following sides are labeled: opposite, adjacent and hypotenuse B hypotenusec A b side adjacent to angle A cos A = adjacent Side a opposite angle A C = hypotenuse sin A = opposite hypotenuse = b c a c tan A = opposite adjacent = a b Trigonometric Ratios • If you were standing at angle B, you would have to relabel the sides of opposite, adjacent and hypotenuse B hypotenusec A b side opposite to angle B cos B = adjacent Side a adjacent angle B C = hypotenuse sin B = opposite hypotenuse = a c b c Tan B = opposite adjacent = b a The famous Indian… SOHCAHTOA Ex. 1: Find sin, cos and tan of angle S Ratio sin S = cosS = tanS = opposite S R hypotenuse adjacent 13 5 hypotenuse opposite adjacent T 12 S Ex.2: Find the sin, cos and tan of angle R Ratio sin R = cosR= tanR = R opposite hypotenuse adjacent hypotenuse opposite adjacent R 13 5 T 12 S 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!!! Let’s find angle S. Ratio sin S = cosS = tanS = opposite S R hypotenuse adjacent 13 5 hypotenuse opposite adjacent T 12 S Now let’s find the angle measure from a previous example Ratio sin R = cosR= tanR = R opposite hypotenuse adjacent hypotenuse opposite adjacent R 13 5 T 12 S Examples: Given the triangles below, find the missing angle measure to the nearest degree 6 2 6 8 ? 10 ? Practice: Solve for the missing variables 1.) 2.) 7 12 x⁰ 26⁰ m 16 9 3.) 30 4.) y z p 15 40⁰ (No decimal answers in 4)