Right Triangle 3 Tangent Sine and Cosine Finding

Right Triangle 3 Tangent, Sine and Cosine Finding the length of a side of a Right Triangle

• In this activity we will learn about the ratios of the lengths of the sides of a right triangle. • The first ratio is called the Tangent ratio. It is defined as: C Tangent of B = leg opposite B leg adjacent B This is abbreviated as: Tan B = opp adj B A

• Find the tangent ratio for B C Tan B = opp adj Tan B =3 4 Tan B =. 75 5 B 3 4 A

• The Second Ratio that you will discover is called the Sine Ratio. It is defined as: Sine of B = leg opposite B hypotenuse This is abbreviated as: Sin B = opp hyp C B A

C • Find the sine ratio for B 5 Sin B = opp hyp Sin B = 3 5 Sin B =. 6 B 3 4 A

• The third ratio to discover is called the Cosine ratio. It is defined as: Cosine of B = leg adjacent B hypotenuse This is abbreviated as: Cos B = adj hyp B C A

• Find the Cosine ratio for B C Cos = adj hyp Cos B = 4 5 Cos B =. 8 5 B 3 4 A

Ask your teacher to tell you the story of Chief Soh. Cah. Toa! On your worksheet do # 1 - 10

• You can use your scientific calculator to find the trigonometric ratio associated with an angle. Your calculator must be in degrees. . 4848 Sin 29 = _____ On your worksheet do # 11 – 16. • You can use the inverse key on your scientific calculator to find the angle associated with a trigonometric ratio. 15 Tan _____° =. 2679 On your worksheet do # 17 -22

• We Can use Trig ratios to find missing sides of right triangles. • Which trig ratio should be used? Tangent • What is the Setup? Tan 37° = X 250 X = 188. 4 X 250 37°

• What if you need to find an angle of a right triangle? We can use trig ratios and the inverse key. • What trig ratio should be used to find the measure of X? Cosine X • What is the setup? 15 Cos X = 15 17 X = Cos-1 (15 17) X = 28° 17

Practice Problems Find the missing side 1. Tan 40° = a / 5 40 Tan 40° (5) = a 5 . 8391(5) = a a a = 4. 195 Sin 63° = 120 2. x x x (Sin 63°) = 120 x= 63 120 sin 63° x = 134. 679

3. Cos 18° = 2500 x 2500 Cos 18° (2500) = x 18 x = 2377. 6 x 4. a Tan 15° = 6 15 a 6 a (Tan 15° ) = 6 a = 6 (Tan 15°) a = 22. 39

Find the missing angles 5. 3 Tan x = 4/ 3 x 4 x = Tan -1 (4/3) x = 53. 13° x = 53° 6. Cos x = 10 / 15 15 x = cos -1 (10 / 15) x 10 x = 48. 189° x = 48°

7. x 2 Sin x = 2 / 12 x = sin -1 (2 / 12) 12 x = 9. 6 ° x = 10 ° 8. Tan x = 5 / 12 5 x = Tan-1 (5/12) x 12 x = 22. 61° x = 23°

Homework: p. 529(22 -26 even, 32 -36 even, 37 -43) p. 538(20, 30 -35)