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Tangent Ratio Labelling Right Triangles Theta: the symbol we will use to represent an unknown angle. Ө Ө Hypotenuse Adjacent Opposite Definitions Hypotenuse: The longest side of a right triangle. It is always across from the 90 degree angle. Adjacent side: Always the side that is attached to or touching the theta symbol Ө Opposite Side: Always the side that is across from the theta symbol. It is not touching Ө Ex 1) Label the triangle with HYP, ADJ, and OPP Hypotenuse Opposite Ө Adjacent Ex 2) Place Ө in the correct angle. Adjacent Opposite Ө Hypotenuse HYP OPP Ө ADJ Ratios When have right triangle, and we have 1 given Step 1:we label theasides HYP OPP ADJ side and 1 given angle, and we need to find the Step 2: Choose either Sin, SIN, Cos orCOS Tan or (depending missing sides, we use TAN. on which side is given and which side you need to find) Step 3: Write out the formula with Sin, Cos or Tan Step 4: Insert the information that has been given in the question (the side length and the angle). Tangent Ratio (TAN) Tan θ = Opposite side Adjacent side If you have a triangle, and you are given a measurement and a variable for the OPPOSITE SIDE and the ADJACENT SIDE, then you need to use the TAN function on your calculator to find the missing side. Trigonometric Ratios Tangent Ratio Step 1: Label sides Tan A = Opposite Adjacent Step 2: Choose Sin, Cos, Tan Step 3: Write out formula A 45 ADJ Step 4: Insert the given information (A or Ө is always an angle) HYP 13cm Step 5: Find the missing side (x). Use cross-multiplication B C x cm OPP Tan 45o = x cm 13cm Ex 1) Write an equation that you can use to find the value of x. A OPP Tan C= Opp Adj D ADJ Tan 30= x cm 11cm x 5cm OPP F X cm 30 E B 30 11 cm ADJ C Tan F= Opp Adj Tan 30= 5 cm x cm Ex 2) Find Tan A. Keep your answer as a fraction. Tan A = Opposite Adjacent A 5cm Tan A= 7cm 5cm √74 cm B ADJ 6√3 cm 6cm B OPP C 7cm A 12cm C Ex 3) Find the value of x. 45 32 cm 15cm 60 x x Class Work Page 560 #1, 2, 4 Page 561 #13-15 Sine and Cosine Ratios Sine Ratio If you have a triangle, and you are given a measurement and a variable for the OPPOSITE SIDE and the HYPOTENUSE, then you need to use the SIN function. Sin Ө = Opposite Side Hypotenuse Trigonometric Ratios Ex 1) Write an equation for Sin A. Find the value of x. Sin A = Opp Hyp A Sin 30 = x cm 10 cm 30 10cm 10 cm (Sin 30) = x cm 1/2 x 10 = x x = 5 cm B x cm C Ex 1) Write an equation for Sin A. Find the value of x. B X cm 12cm 60 C A Cosine Ratio If you have a triangle, and you are given a measurement and a variable for the HYPOTENUSE and the ADJACENT SIDE, then you need to use the COS function. Cos Ө = Adjacent Side Hypotenuse Trigonometric Ratios Write an equation for Cos A A 7cm B B 12cm 11cm C C A 5cm Ex 1) Write an equation for Cos A. Find the value of x. A Cos A = ADJ HYP 45 7cm Cos 45 = 7cm x cm √2 = 7 2 x x cm √2 x = 14 B C x=7√2 Ex 1) Find the value of x. Choose Sin, Cos or Tan. B 11cm 6 cm 30 C A x cm Ex 2) Write equations for Sin A and Cos A. A 15cm 17cm B A 8cm C 10 cm B 8cm 6 cm C Trigonometric Ratios SOH CAH TOA Sin A = Opp Hyp Cos A = Adj Hyp Tan A= Opp Adj Class Work • Page 563 #1-3 • Page 564 # 4-6 • Page 566 #11-16