1 / 16

Finding the length of a side of a Right Triangle

Right Triangle 3 Tangent, Sine and Cosine. Finding the length of a side of a Right Triangle. C. A. B. This is abbreviated as: Tan B = opp. adj. Trigonometric Ratios. In this activity we will learn about the ratios of the lengths of the sides of a right triangle.

shelby-conley
Download Presentation

Finding the length of a side of a Right Triangle

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

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

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

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

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

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

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

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

  9. 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

  10. X 37° Tan 37° = X 250 250 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 = 188.4

  11. X 17 15 Cos X = 15 17 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? Cosine • What is the setup? X = Cos-1 (1517) X = 28°

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

  13. 3. 2500 18 x a 4. 15 6 Cos 18° = x 2500 Cos 18° (2500) = x x = 2377.6 Tan 15° = 6 a a (Tan 15° ) = 6 a = 6 (Tan 15°) a = 22.39

  14. 5. 3 x 4 6. 15 x 10 Find the missing angles Tan x = 4/ 3 x = Tan -1 (4/3) x = 53.13° x = 53° Cos x = 10 / 15 x = cos -1 (10 / 15) x = 48.189° x = 48°

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

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

More Related