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

Trigonometric Ratios 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: A B C Tangent of B = leg opposite B leg adjacent B This is abbreviated as: Tan B = opp adj

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

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

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

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

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

Trigonometric Ratios Ask your teacher to tell you the story of Chief SohCahToa! On your worksheet do # 1 - 10

Trigonometric Ratios 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

Trigonometric Ratios We Can use Trig ratios to find missing sides of right triangles. Tangent Which trig ratio should be used? What is the Setup? X 37° 250 Tan 37° = X 250 X = 188.4

What trig ratio should be used to find the measure of X? Trigonometric Ratios 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? 17 15 X Cosine What is the setup? Cos X = 15 17 X = Cos-1 (1517) X = 28°

Practice Problems Find the missing side 5 40 a 1. Tan 40° = a / 5 Tan 40° (5) = a .8391(5) = a a = 4.195 2. 120 x 63 Sin 63° = 120 x x (Sin 63°) = 120 x = 120 sin 63° x = 134.679

3. Cos 18° = x 2500 Cos 18° (2500) = x x = 2377.6 4. a Tan 15° = 6 a 18 2500 x Cos 18° = x 2500 Cos 18° (2500) = x x = 2377.6 4. 6 15 a Tan 15° = 6 a a (Tan 15° ) = 6 a = 6 (Tan 15°) a = 22.39

Find the missing angles 5. 3 4 x Tan x = 4/ 3 x = Tan -1 (4/3) x = 53.13° x = 53° 15 x 10 6. Cos x = 10 / 15 x = cos -1 (10 / 15) x = 48.189° x = 48°

7. Sin x = 2 / 12 x = sin -1 (2 / 12) x = 9.6 ° x = 10 ° 8. 5 x Tan x = 5 / 12 x = Tan-1 (5/12) x = 22.61° x = 23°

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