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Add hypotenuse, the three proportions, Pythagorean Thm. and Converse(obtuse, acute), multiply fractions vs. proportions, 45-45-90 and 30-60-90 formulas,

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Presentation on theme: "Add hypotenuse, the three proportions, Pythagorean Thm. and Converse(obtuse, acute), multiply fractions vs. proportions, 45-45-90 and 30-60-90 formulas,"— Presentation transcript:

1 Add hypotenuse, the three proportions, Pythagorean Thm. and Converse(obtuse, acute), multiply fractions vs. proportions, 45-45-90 and 30-60-90 formulas, Pythagorean triple, sin, cos, tangent to vocab list

2 Geometry 8.6 The Sine and Cosine Ratios

3 Sine ratio = opposite leg adjacent leg hypotenuse opposite leg adjacent leg A B Sine of { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/14/4212883/slides/slide_3.jpg", "name": "Sine ratio = opposite leg adjacent leg hypotenuse opposite leg adjacent leg A B Sine of

4 Cosine ratio = opposite leg adjacent leg hypotenuse opposite leg adjacent leg A B Cosine of { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/14/4212883/slides/slide_4.jpg", "name": "Cosine ratio = opposite leg adjacent leg hypotenuse opposite leg adjacent leg A B Cosine of

5 Easily remember all 3 trig ratios! SS o h CC a h TT o a sin opposite adjacent cos tan hypotenuse

6 45 B 24 51 A A 15 12 9 B B 5 10 A 6 AB I. Express Sin A, Sin B, Cos A and Cos B as ratios. 1.2. 3.4.

7 1) Express Sin A, Sin B, Cos A, and Cos B as ratios. 24 51 45 B A O A H O A

8 Answers 2) sin A = 3/5, sin B = 4/5, cos A = 4/5, cos B = 3/5 3) sin A = 1/2, sin B =, cos A =, cos B = 3/5 4) All ratios are

9 Exercises 13. Find the value of x and y to the nearest tenth. y x 52 o 34 (34).7880 ≈ x (34).6157 ≈ y O A H

10 16 x y 43  y 34 52  x 6 47  x x y y xx 75  44 60 37 nn nn x 13 n  5 17. II. Find the value of x and y to the nearest tenth. 13.14. 15.16. 18.

11 Exercises 15. Find the value of x and y to the nearest tenth. x x 6 47 o y sin 47 = 6 x.7314 ≈ 6 x x(.7314) ≈ 6 x ≈ 6.7314 x ≈ 8.2 a tan 47 = 6 a 1.0724 ≈ 6 a a(1.0724) ≈ 6 a ≈ 6 1.0724 a ≈ 5.6 y ≈ 11.2 O A H

12 Exercises 17. Find n to the nearest degree. 60 37 nono H A cos n = 37 60 cos n ≈.6166 n ≈ 52 o

13 HW 14. x ≈ 11.7, y ≈ 10.9 16. x ≈ 85, y ≈ 82.1 18. x = 12, n ≈ 67 o P. 313 CE (1-13)Odds P. 314 (1-17) Odds


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