1.  ABC ~  MNP ~  DEF P D N M 0.73 1.27 5 1.82 Find the ratios. Round to 4 decimals places. D E F 4 4√2 A B C 2 2√2 M N P 3 3√2 C B A 2 20 o 3.5 20 o E F

2. Right Triangles Day 6 – Trigonometry

3. Answers to Quiz 1) x = 4 2) x = 2√13 ≈ 7.21 3) a = 10√2; b = 10 4) m = 2√6; n = 2√2 5) Bottom diag: 20” Large meas: 22.36” 6) 5 2 + 5.25 2 = 7.25 2 25 + 27.56 = 52.56 52.56 = 52.56 Yes, the sandbox is straight. 7)

4. Answers to Quiz 8) AB = 3 BD=3 √3 D(8 - 3 √3, 3) D(2.8, 3) m: 6) B A

5. Objective  To perform calculations using trigonometric ratios

6. Homework  Trigonometry Worksheet  Need help? Look in your book – Section 9.5

7. Trigonometric Ratios  All right triangles with one angle congruent are ________  Because the triangles are similar, the sides are ______________ xoxo similar proportional opposite hypotenuse adjacent TRIGONOMETRIC RATIOS Sine (sin)sin x = opposite hypotenuse cosine (cos)cos x = adjacent hypotenuse tangent (tan)tan x = opposite adjacent SOH – CAH - TOA

8. Trigonometric Ratios  All right triangles with one angle congruent are ________  Because the triangles are similar, the sides are ______________ xoxo similar proportional opposite hypotenuse adjacent TRIGONOMETRIC RATIOS Sine (sin) sin x = opposite hypotenuse Cosine (cos) cos x = adjacent hypotenuse Tangent (tan) tan x = opposite adjacent SOH – CAH - TOA sin y = opposite hypotenuse cos y = adjacent hypotenuse tan y = opposite adjacent yoyo

9. Find the trigonometric ratios for all acute angles AA hypotenuse CC opposite adjacent

10. Use a calculator to approximate the ratios  tan 79 o =  sin 24 o =  cos 79 o =  sin 87 o =

11. Find the side of the triangle adjacent hypotenuse opposite SOH-CAH-TOA tan x = opposite adjacent Which ratio should be used? Identify sides based on the known angle Fill in all known information tan 66 = x 39 Simplify ratio and turn into a proportion 2.2460 = x 39 1 Solve x = 87.6

12. Find the side of the triangle adjacent hypotenuse opposite SOH-CAH-TOA sin x = opposite hypotenuse Which ratio should be used? Identify sides based on the known angle Fill in all known information sin 55 = 25 x Simplify ratio and turn into a proportion 0.8190 = 25 x 1 Solve x = 30.5