Agenda 2/25/13 1) Bell Work 2) Outcomes 3)Finish Solving Right Triangle Notes(9.6) 4) Review quiz concepts 5) Problem Packet(possibly group work) tablet password = cosine

Bell Work 2/27/13 1)Use Pythagorean Theorem 2) Use Special Right x = _____ y = _____ a = _____ b = ____ 3) Solve for the missing side using Trig Ratios A) B) w = _____ x = _____

Outcomes I will be able to: 1) Use Properties of special right triangles 2) Understand Trigonometric Ratios 3) Use Pythagorean Theorem 4) Understand proportions in triangles

9.6 Notes – Solving Right Triangles What does it mean to solve a right triangle? Solve a Right Triangle – Determine the measures of all six parts of a right triangle (3 angles and 3 sides). You can solve a right triangle if you know: 1. Two side lengths 2. One side length and one acute angle measure

Inverses 1. If sin A = x, then _________________. 2. If cos A = y, then _________________. 3. If tan A = z, then _________________. ***You can use either your calculator or your trig table to determine the angle measure.

Examples Use a calculator or trig ratio table to find the following. 1. Sin A = .9205 2. Cos B = .1392 3. Tan C = 11.4301 4. Cos A = .9659

Examples 5. Solve the right triangle. Round decimals to the nearest tenth. What trig ratios do we have to determine angle A and C? From A: Cos A = 8/10 = .8 From C: Sin C = 8/10 = .8 Look at trig table to determine the angle measures Angle A = 36° Angle C = 54° 8 10 A B C

Examples 6. Solve the right triangle. Round decimals to the nearest tenth. What trig ratios do we have? Looking at a Sin 65 = a/20 Convert Sin 65 to decimal using chart .9063 = a/20 x 20 x 20 18.1 = a Cos 65 = b/20 – repeat the process .4226 = b/20 8.5 = b a 65º 20 x Y Z b

Examples 7. Solve the right triangle. Round decimals to the nearest tenth. What trig ratios do we have? Cos 20 = y/15 .9397 = y/15 14.1 = y Sin 20 = x/15 .3420 = x/15 5.1 = x T S R 15 20º x y

Examples 1 1.8 What is the height of the balloon? Tan 28° = h/1.8 8. During a hot air balloon flight, Willie and Nia look upwards and see the balloon, as shown in the diagram below. The angle of elevation from Nia is 28˚ and she is 1.8 miles from the spot on the ground directly below the balloon. What is the height of the balloon? Tan 28° = h/1.8 h = .96 Willie is 2.8 miles from Nia. Find the angle of elevation from Willie. Tan W = .96/1 m ∠W = 44° W N h 28° 1 1.8