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#12 Opener Solutions #1 A squirrel drops a nut from a tree. The nut would normally drop 15 feet vertically, but because of the wind it travels along a path that forms a 17º angle with the vertical. How far from the tree does that nut land? (Round to the nearest hundredth.) 17º 15 feet x 4.59 feet #2 A television antenna sits atop a building. From a point 150 feet away from the base of the building, the measurement of the angle of elevation to the top of the antenna is 75º. From the same point, the measurement of the angle of elevation to the bottom of the antenna is 68º. How tall is the antenna? tan 75 = x+ y 150 x = antenna 75º Whole Angle y= building 68º 150 feet y and tan 68 = 150 189 feet #12 Notes / Review Chapter 13 #6-#11 Doors vs. Windows One person from each team will be called on. If correct, 1 goodie from the Amazing Bag of Goodies and 3 bean bag tosses. Bean Bag Toss 3 tosses each 3 points for in the hole 2 points for leaning over the hole 1 point for on the box **Clean up after yourself when you are done. Grade Book Winning team = 6/5 in grade book 2nd place = 5/5 in grade book Target Goal: The students will be able to use right triangles to find trigonometric values and solve problems involving right triangles using right triangle trigonometry. #1 Solve the right triangle. (Draw a picture.) a = 11 inches b = 22.3 inches (Round to the nearest tenth.) c = 24.9 inches A = 26.3º B = 63.7º Target Goal: The students will be able to use right triangles to find trigonometric values and solve problems involving right triangles using right triangle trigonometry. #2 Solve the right triangle. (Draw a picture.) A = 22º c = 42 meters B = 68º a = 15.7 meters b = 38.9 meters #3 Target Goal: The students will be able to solve word problems using right triangle trigonometry. Application: Show all work. Dave is 200 feet away from a tower and he has determined the angle of elevation to the top of the tower to be 32º. Find the height of the tower to the nearest foot. x 32º 200 tan 32 = x 200 125 feet #4 Target Goal: The students will be able to solve word problems using right triangle trigonometry. Application: Show all work. Two cities are 10 miles apart. An object is seen hovering in the sky above the line joining the two cities. The angles of elevation from the cities to the object are 24º and 40º. What is the height of the object above the ground? (Round to the nearest tenth.) * object x 40º 10-a a 24º * object x 40º tan 24 = 10-a x a a and tan 40 = 24º x 10−a 2.9 miles #5 Application: Target Goal: The students will be able to solve word problems using right triangle trigonometry. (Show all work.) A man is in a boat that is floating 175 feet from the base of a 200 foot cliff. What is the angle of depression between the cliff and the boat? Round to the nearest tenth. tan x 200 = 175 x 200 feet x 175 feet 48.8º Target Goal: The students will be able to find values of trigonometric functions for general angles. #6 The terminal side of θ in standard position contains the point (8, 4). Find the exact values of the six trigonometric functions of θ . sinθ = 5 5 cosθ = 2 5 5 tanθ = 1 2 cscθ = 5 secθ = 5 2 cotθ =2 Target Goal: #7 The students will be able to find values of trigonometric functions for general angles. The terminal side of θ in standard position contains the point (8, -15). Find the exact values of the six trigonometric functions of θ . sinθ =−15 17 cosθ = 8 17 tanθ =−15 8 cscθ =−17 15 secθ = 17 8 cotθ =− 8 15 Target Goal: #8 The students will be able to find values of trigonometric functions for general angles. The terminal side of θ in standard position contains the point (-4, -3). Find the exact values of the six trigonometric functions of θ . sinθ =− 3 5 cscθ =− 5 3 cosθ =− 4 5 secθ =− 5 4 tanθ = 3 4 cotθ = 4 3 Target Goal: #9 The students will be able to find values of trigonometric functions for general angles. The terminal side of θ in standard position contains the point (0, 10). Find the exact values of the six trigonometric functions of θ . sinθ =1 cosθ =0 cscθ =1 secθ =undefined tanθ =undefined cotθ =0 Target Goal: #10 The students will be able to find values of trigonometric functions by using reference angles. • Sketch a 135º angle. • Name the reference angle. • Put the correct proportions for the reference angle. • Find the exact value for the sin 135º and tan 135º. Reference Angle = 45º sin 135º = 2 tan 135º = -1 2 1 2 45º -1 Target Goal: #11 The students will be able to find values of trigonometric functions by using reference angles. • Sketch a -330º angle. • Name the reference angle. • Put the correct proportions for the reference angle. • Find the exact value for the cos -330º and csc -330º. Reference Angle = 30º cos -330º = 3 csc (-330º) = 2 2 2 30º -330º 3 1 Target Goal: #12 The students will be able to find values of trigonometric functions by using reference angles. • Sketch a − 2π angle. 3 • Name the reference angle. • Put the correct proportions for the reference angle. • Find the exact value for the sec − 2π and cot − 2π . 3 3 Reference Angle = 60º=π 3 2 π 2 π sec − =-2 cot − = 3 3 3 3 -1 − 3 60º 2 Target Goal: #13 The students will be able to find values of trigonometric functions by using reference angles. • Sketch a 13π angle. 4 • Name the reference angle. • Put the correct proportions for the reference angle. • Find the exact value for the sec 13π and cot 13π . 4 4 Reference Angle = 45º=π 4 sec 13π = − 2 cot 13π = 1 4 4 -1 -1 45º 2 Target Goal: The students will be able to solve logarithmic equations #14 Solve: log 3x + log 4 = log 36 3 3 3 3 Do HW #12 Worksheet (optional) Solutions on Line •It is your job to check the HW solutions on line. •See me before school in the math office with any questions. • See the board for the quiz #6-#12 date. • The quiz is individual with the use of your foldable. • 36 points