Tangent Ratio

Labelling Right Triangles Theta: the symbol we will use to represent an unknown angle. Ө Hypotenuse Adjacent Opposite Ө

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 Opposite Side: Always the side that is across from the theta symbol. It is not touching Ө Ө

Ex 1) Label the triangle with HYP, ADJ, and OPP Hypotenuse Opposite Adjacent Ө

Ex 2) Place Ө in the correct angle. Adjacent Opposite Hypotenuse Ө HYP OPP ADJ Ө

Ratios When we have a right triangle, and we have 1 given side and 1 given angle, and we need to find the missing sides, we use SIN, COS or TAN. Step 1: label the sides HYP OPP ADJ   Step 2: Choose either Sin, Cos or Tan (depending 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 Tan A = Opposite Adjacent Tan 45o = x cm 13cm HYP ADJ Step 1: Label sides Step 2: Choose Sin, Cos, Tan Step 3: Write out formula Step 4: Insert the given information (A or Ө is always an angle) Step 5: Find the missing side (x). Use cross-multiplication Tan A = Opposite Adjacent A 45 13cm B C x cm HYP ADJ Tan 45o = x cm 13cm OPP

Ex 1) Write an equation that you can use to find the value of x. Tan C= Opp Adj Tan 30= x cm 11cm D x 5cm F 30 E A X cm B 30 C 11 cm ADJ OPP OPP ADJ 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 √74 cm B C 7cm Tan A= 7cm 5cm ADJ OPP B 6cm 6√3 cm A 12cm C

Ex 3) Find the value of x. 45 15cm x 32 cm 60 x

Class Work Page 560 #1, 2, 4 Page 561 #13-15

Sine and Cosine Ratios

Sine Ratio Sin Ө = Opposite Side Hypotenuse 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 Sin 30 = x cm 10 cm 10 cm (Sin 30) = x cm 1/2 x 10 = x x = 5 cm A 30 10cm B C x cm

Ex 1) Write an equation for Sin A. Find the value of x. B X cm 12cm 60 C A

Cosine Ratio Cos Ө = Adjacent Side Hypotenuse 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 7cm 12cm B C B 11cm C A 5cm

Ex 1) Write an equation for Cos A. Find the value of x. 45 7cm x cm B C Cos A = ADJ HYP Cos 45 = 7cm x cm √2 = 7 2 x √2 x = 14 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 B 17cm 8cm C A 10 cm 8cm B 6 cm C

TOA Tan A= Opp Adj SOH Sin A = Opp Hyp CAH Cos A = Adj Trigonometric Ratios SOH Sin A = Opp Hyp CAH Cos A = Adj TOA Tan A= Opp Adj

Class Work Page 563 #1-3 Page 564 # 4-6 Page 566 #11-16