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Name: Ms. D’Amato Date: Block: Trigonometric Ratios The word “trigonometry” means “ .” There are 6 measurements in a triangle: angle measures and side lengths. To “solve a triangle” means to find the unknown angle measures and the unknown side lengths. Example 1: Solve ∆ABC. A To solve ∆ABC, we need to find the missing angle and the missing sides: 5 mA = ____° Example 2: CB = _____ AB = _____ B E Solve ∆GEO. To solve ∆GEO, we need to find the missing angle and the missing sides: mE = _____° 30 C GE = _____ 5 2 GO = _____ G 45° O If the triangle is not a special right triangle, we need to know a little trigonometry. There are 6 ratios in trigonometry. Reminder: ratio means fraction! In geometry we use only 3 of the trig ratios: sine (abbreviation is sin) cosine (abbreviation is cos) tangent (abbreviation is tan) pronounced the same as “sign” (The other 3 ratios are cosecant, secant and cotangent.) Definitions: Example 3: a.) sine of an acute angle: opposite leg hypotenuse cosine of an acute angle: adjacent leg hypotenuse tangent of an angle: opposite leg adjacent leg Find the missing side length and the trig ratios. If possible, leave your answers in simplest fraction form. P 8 Z R b.) 10 6 Y 5 X Q QR = ______ sin Q = _____ XY = ______ sin Z = ______ cos Q = _____ sin R = _____ cos Y = _____ cos Z = ______ tan Q = _____ tan R = _____ tan Y= _____ tan Z = ______ SohCahToa helps us remember the three trig ratios: S= o h C= a h T= o a Example 4: Now let us use Trig Functions to find missing sides! a.) Steps: 1. Label the given sides 2. Determine the Trig Function 3. Set up proportion 4. Solve using crossmultiplication b.) c.) d.) e.) Example 5: Find the area of the triangle below. Example 6: Find the perimeter of the triangle below. Example 7: Solve for all of the variables.