TRIGONOMETRY Triangle Measurement The Triangle Angles Capital Letters

TRIGONOMETRY “Triangle Measurement”

The Triangle Angles : Capital Letters Sides: Lower Case Letters B c a C b A

The Triangle Opposite: Across From Adjacent: Part of A Hypotenuse: Across From the Right Angle

SOHCAHTOA opposite hypotenuse A

SOHCAHTOA hypotenuse adjacent A

SOHCAHTOA Opposite A Adjacent

Labeling Triangles Label the triangle according to angle A. Label the opposite side, adjacent side and the hypotenuse. Then name Angle B, side a, b, and c. b A c a B

Calculator Practice Determining trig values… Given the angle measure, use the sine (sin), cosine (cos) and tangent (tan) buttons, determine the trig values of each. Round to 4 decimal places. 1. Sin 52° =. 788010754 . 7880 2. Cos 62° =. 469471563 . 4695 3. Tan 25° =. 466307658 . 4663

Calculator Practice Determining Angle Measures… Given the trig values, use the inverse function to determine the angle measures. Round to the nearest degree. 1. Sin. 9877 = 81. 00427139 2. Cos. 9816 = 11. 0081596 81º 11º 3. Tan. 8391 = 40. 0000124 40º

Solving Triangles Solving triangles means to find all of the angles and all of the sides. Given the following triangle, find the missing side, set up the ratios, and find the missing angles. 8 cm 10 cm A x cm 82 + x 2 = 102 x= 6 64 + x 2 = 100 Sin A = 8/10 x 2 = 100 - 64 Cos A = 6/10 x 2 = 36 Tan A = 8/6 x=6 Angle A = 53° Angle B = 90 - 53 = 37°

Mnemonics 1. "Tommy On A Ship Of His Caught A Herring" (probably more common in Great Britain than the United States). 2. 3. 4. "Oscar Has A Hold On Angie. ” "Oscar Had A Heap of Apples. ” "The Old Army Colonel And His Son Often Hiccup" (which gives the functions in the order tangent, cosine, sine). 5. "Studying Our Homework Can Always Help To Obtain Achievement. ”

Bonus Assignment: Create a Mnemonic to remember SOHCAHTOA