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5.2 Apply the Tangent Ratio Pg. 157 Labeling a Triangle B c A a b C Vertices are labeled with Upper Case CAPITAL Letters Sides are labeled with lower case letters, and correspond to the angle opposite of the side Remember the sum of all angles in a triangle is 180° Two angles are complimentary angles if their sum is 90° The Tangent Ratio B c A a b C • Let ABC be a right triangle with acute A . The tangent of A (written as tan A) is defined as follows: length of leg opposite A BC tan A length of leg adjacent to A AC Real Life Problem How tall is the tree if a 6 ft. tall man is 60 ft. from the base and has an angle of elevation of 37° We will use trigonometry to solve Trigonometry • Trigonometry – the study of the ___________ of _____________ • Trigonometric Ratio – the ___________ of ___________ of ____ sides of a _____________ triangle. To find missing lengths of a right triangle: Given: 1) 2 sides To Find: 1 side Use: Pythagorean Theorem 2) 1 side Other 2 sides a) Use Special Right Triangle IF IT IS ONE! b) Use Trig Ratios IF IT ISN’T “SPECIAL”! Trigonometric ratios are great if you’re only given 2 pieces of information IN ADDITION TO ALREADY HAVING THE _________ angle. Example: 1) 2) x 37° 18 Real Life Problem How tall is the tree if a 6 ft. tall man is 60 ft. from the base and has an angle of elevation of 37° Homework Pg. 161, 1 – 20 all 5.3 Apply the Sine and Cosine Ratios Pg. 163 The Sine and Cosine Ratios B c A a b C • Let ABC be a right triangle with acute A . The sine of A and the cosine of A (written as sin A and cos A) is defined as follows: length of leg opposite A BC sin A length of hypotenuse AB length of leg adjacent to A AC cos A length of hypotenuse AB 3 Basic Trigonometric Ratios • Remember, a ratio compares two things. • We will be comparing 2 ____________ Need a reference Name Abbreviation Sine sin sin ( ) Cosine cos cos ( ) Tangent tan tan ( ) The reference angle is never _________ AGAIN, YOU CANNOT TAKE THE SIN, COS, OR TAN OF ANYTHING UNLESS YOU HAVE A REFERENCE ANGLE YOU’RE USING! So how do you use these Trigonometric Ratios? Its all about the relationships You’ve got ________, ________, and _______ sides with trig ratios. SOH – CAH - TOA a=4 b=5 c=3 sin A = sin C = cos A = cos C = tan A = tan C = A b=5 C a=4 c=3 B Why not sin B, cos B, or tan B ? Homework Pg. 161, 1 – 20 all