Name: Date: School: Facilitator: 8.04 Geometric Probability Find the geometric probability for each question if each point is selected randomly from segment AE. Simplify your answers. 1. P(point X is on AB)= Answer: 2. P(point X is on BC)= Answer: 3. P(point X is on CD)= Answer: 4. P(point X is on DE)= Answer: Find the geometric probability for each question if each point is selected randomly from the figure. Include all information needed. 5. P(point X is in the shaded area)= Shaded area: Entire area: Answer: 6. P(point X is in the shaded area)= Shaded area: Entire area: Answer: 7. P(point X is in the blue circle)= Shaded area: Entire area (black circle): Answer: 8. P(point X is in the blue circle)= Shaded area: Entire area (red rectangle): Answer: Name: School: Date: Facilitator: 8.03 Special Right Triangles Find the value of the indicated side. You can copy and paste the following notation as needed: 3 or 2 1. Given hypotenuse 8, find the short leg: a = Show your work: 2. Given the short leg a = 7, find the long leg: b = Show your work: 3. Given short side a = 3, find the hypotenuse: c = Show your work: 4. Given the long leg b = Show your work: , find the hypotenuse: 5. Given the leg is 5, find the other leg: Show your work: 6. Given the hypotenuse = 6 , find the leg: Show your work: Name: Date: School: Facilitator: 9.01 Trigonometric Ratios 1. Find the values of the following in simplest fraction form then divide to represent in decimal form. AB = 13, AC = 12, BC = 5 Fraction form Sin A = Cos A = Tan A = Decimal form Sin A = Cos A = Tan A = 2. Use the Online Trigonometric Table of Values to find the following: Sin 10o = Tan 45o = Cos 80 o = 3. Use a scientific calculator to find the following values. (Web 2.0 Calc) Sin 80 o = Cos 45o = Tan 77o = 4. Open the Trig Functions activity. Use the interactive to answer the following questions. How does the value of sinA change as How does the value of cosA change as increases and decreases? increases and decreases? What happens to the value of tanA as you increase How do the reciprocal values change compared to the other functions? Which values are always less than 1? When are sine and cosine equal? ? 5. Identify the relationship between the sine and cosine of complementary angles. Using the Online Trigonometric Table of Values or the Trig Functions activity, you can start by stating the sine and cosine for the complementary angles 40 and 50 sin 40 = cos 40 = sin 50 = cos 50 = Think of two complementary angles and list the sine and cosine for each. Complementary angles and sin = cos = sin = cos = How does the value of sine and cosine of complementary angles relate? Explain in your words why this relationship of sine and cosine holds for complementary angles. Name: Date: School: Facilitator: 9.02 Solving Right Triangles For the problems below, show all of your work. 1. Solve the triangle for side b. Round to nearest tenth. Show your work. Answer: Show your work below. 2. Two trees stand opposite one another, at points A and B, on opposite banks of a river. Distance AC along one bank is perpendicular to BA, and is measured to be 150 feet. Angle ACB is measured to be 61. How far apart are the trees; that is, what is the width w of the river? Answer: Show your work below. 3. Solve the right triangle ABC given that side c = 17 cm and side b = 15 cm. Answer: a =, A = b =, B = c =, C = Show your work below Name: Date: School: Facilitator: 9.03: Law of Sine and Cosine Be sure to complete problems 1-3 which apply the Law of Sines and Law of Cosines, then for problems 4-5 complete the proofs for each law. 1. Use Law of Sines to find the missing side b: Show your work: 2. Use Law of Cosines to find the missing side b: Show your work: 3. Decide whether the Law of Sines or the Law of Cosines can be used to find the measure of c: Find c: Show your work: 4. PROOF: Justify each statement in order to derive the Law of Sines. Given: CD is an altitude of ABC Prove: sin A sin B a b Proof: Statements 1. CD is an altitude of ABC 2. ACD and CBD are right ' s h h b a 4. b sin A h; a sin B h 5. b sin A a sin B sin A sin B 6. a b 3. sin A ;sin B Reasons 1. 2. 3. 4. 5. 6. Matching for reasons: a. Property of division b. Definition of Sine c. Given d. Property of Multiplication e. Definition of altitude f. Substitution 5. PROOF: Justify each statement in order to derive the Law of Cosine by completing the reasons Given: h i s an altitude of ABC Prove: b 2 a 2 c 2 2ac cos B Proof: Statements 1. h is an altitude of ABC 2. ACD and CBD are right ' s 3. b 2 (c x) 2 h 2 4. b 2 c 2 2cx x 2 h2 5. x 2 h2 a 2 Reasons 1. 2. 3.Pythagorean Theorem 4. FOIL method 5. 6. b 2 c 2 2cx a 2 x a 8. a cos B x 9. b 2 c 2 2c(a cos B) a 2 6. Substitution 7. cos B 7. 10. b 2 a 2 c 2 2ac cos B 8. 9. Substitution 10. Matching for reasons: a. Pythagorean Theorem b. Definition of Cosine c. Given d. Property of Multiplication e. Definition of altitude f. Substitution