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Elizabeth Pawelka Geometric Probability 4/11/12 Geometry Lesson Plans Section 9-5: Trigonometry and Area 4/18/12 Pre-Quiz Warm-up (5 mins) Find value of each variable to the nearest tenth. Check your sides with the Pythagorean Theorem. Check angles with Triangle Angle Sum Theorem/Complementary Angles Ask for any questions on sections 9-1/9-2 Quiz on sections 9-1/9-2 (25 mins) Post-Quiz Seat-work (15 mins) “When a Ruler Isn’t Enough” worksheet Reteaching 9-3: p. 109 # 1, 3, 4, 5 p.1 Elizabeth Pawelka Geometric Probability 4/11/12 p.2 Homework Review (10 mins) – ask for any questions on homework Homework (H) p. 484, #1 – 21, 23, 28, 33, 34 Homework (R) p. 484, #1 – 21, 23, 33 Statement of Objectives (5 mins) The student will be able to use trigonometry to find area of polygons. Teacher Input (25 mins) Area of a regular polygon = ½ ap Use trigonometry to find apothem: p = 5 * 8 = 40cm Find measure of central angle: 360/5 = 72 m∠XCY = ½ m∠XCZ = 36. XY = ½ XZ = 4 tan(36) = 4/a a = 4/tan(36) a = 5.5 A = ½ (5.5)(40) = 110.11055 Find area of regular octagon with perimeter of 80. Elizabeth Pawelka Geometric Probability 4/11/12 side = 80/8 = 10 angle = ½(360/8) = 22.5 tan(22.5) = 5/a a = 5/tan(22.5) a = 12.1 A = ½(12.1)(80) = 482.8 in2 Find area of these regular polygons p.3 Elizabeth Pawelka have a, need perimeter: 2x(6) tan(30) = x/6 x = 6 tan(30) x = 3.46 p = 2(3.46)*6 = 41.57 A = ½(6)(41.57) = 124.71 cm2 Geometric Probability 4/11/12 p.4 p = 10 * 12 = 120 need a: central angle = 360/10 = 36 36/2 = 18 tan(18) = 6/a a = 6/tan(18) = 18.466 A = ½(18.466)(120) = 1107.966 = 1108 cm2 Elizabeth Pawelka Geometric Probability Area of Triangles What if you only had m∠A and lengths b and c? Find h: Area of Triangle = ½ b*h h c h = c (sin A) sin A = Area = ½ bc(sin A) Theorem 9-1: Area of a Triangle Given SAS Area of ΔABC = ½ bc(sin A) Find area of this triangle to the nearest hundredth A = ½ 5*9*sin(34) = 12.58 in2 Find area of these triangles to nearest tenth: 4/11/12 p.5 Elizabeth Pawelka A = ½ 7*7*sin(31) = 12.6 ft2 Geometric Probability A = ½ (7*10*sin(44)) = 24.3 m2 4/11/12 p.6 A = ½ * 8*6*sin(61) = 20.99 = 21 in2 Extension: If area of a triangle = ½ b*h and area of a parallelogram = b*h, what is the area of a parallelogram given SAS? Area of a parallelogram = bc(sin A): Find area of this parallelogram to the nearest hundredth A = 10*8*sin(63) = 71.28 m2 (Show Heron’s formula – p. 353: Challenge) Find area of these regular polygons to nearest tenth Elizabeth Pawelka Geometric Probability 4/11/12 p.7 A dodecagon with perimeter = 108 ½(central angle) = ½(45) = 22.5 cos(22.5) = a/10 a = 10*cos(22.5) sin(22.5) = ½ b/10 ½ b = 10sin(22.5) b = 20sin(22.5) p = 8*20sin(22.5) A = ½(16.8)108 = 906.9 cm A = ½ (10*cos(22.5)) * (8*20sin(22.5)) = 282.8 m Closure (5 mins) Today you learned to use trigonometry to find area of polygons. Tomorrow we’ll review for the Chapter Test on Friday. Homework (H) p. 500, # 1 – 18, 20, 21, 23, 25, 27 Homework (R) p. 500, # 1 – 18, 20, 21, 25

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