5B.4 ~ Calculating Sine, Cosine, Tangent, Cosecant, Secant and Cotangent WB: Pgs :1-10 Pgs : 1-7
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1 SECONDARY 2 HONORS ~ UNIT 5B (Similarity, Right Triangle Trigonometry, and Proof) Assignments from your Student Workbook are labeled WB Those from your hardbound Student Resource Book are labeled RB. Do all work from the Student Resource Book (RB) on a separate piece of paper. 5B.1 ~ Proving Theorems about Parallelograms WB: Pg : #1-10 RB: U5-281: #1-10 5B.2 ~ Proving Properties of Special Quadrilaterals WB: Pg. 353: #1-9 5B.3 ~ Defining Trigonometric Ratios & Exploring Sine and Cosine WB: Pgs : #1, 2, 5, 7, 9 Pgs : #1, 3, 5, 7-10 all RB: Pgs. U : #1, 2, 7, 9 Pgs. U : #1, 3, 6, 8-10 all 5B.4 ~ Calculating Sine, Cosine, Tangent, Cosecant, Secant and Cotangent WB: Pgs :1-10 Pgs : 1-7 RB: Pgs. U : 4, 7 Additional Problems: Find the missing angle. Round all answers to the nearest whole number
2 5B.5 ~ Applying Trigonometric Ratios & Proving Pythagorean Identity WB: Pgs : 1-4, 6-8 Pgs : 1-6, 8, 10 (numbers 4 and 5 you only need to find the values for the remaining 2 trigonometric functions using identities, and then find the value of θ) RB: Pgs. U : 1, 6, 7 ANSWERS FOR ASSIGNMENTS: Remember: this is only to check your answers ~ all work must be shown, or no credit will be given!! 5B.1 answers: RB: U5-281 #1-8,( #9 and 10 for Honors)
3 5B.2 answers: 1. Quadrilateral ABCD is a parallelogram and a rectangle. Justification: opposite sides are parallel, adjacent sides are perpendicular, the diagonals bisect each other, and not all four sides are congruent. 2. Quadrilateral EFGH is a kite. Justification: adjacent sides are congruent and the diagonals intersect at a right angle. 3. Quadrilateral IJKL is a parallelogram, a rectangle, a rhombus, and a square. Justification: opposite sides are parallel, consecutive sides are perpendicular, the diagonals bisect each other, and all four sides are congruent. 4. Quadrilateral MNOP is a parallelogram, a rhombus, and a square. Justification: opposite sides are parallel, adjacent sides are perpendicular, the diagonals are perpendicular, and all four sides are congruent. 5. Quadrilateral PQRS is a parallelogram. Justification: opposite sides are parallel, plus the diagonals are congruent and bisect each other. 6. Quadrilateral TUVW is an isosceles trapezoid. Justification: one pair of opposite sides is parallel and the other pair of sides is congruent. 7. Quadrilateral WXYZ is a parallelogram and a rectangle. Justification: opposite sides are parallel, adjacent sides are perpendicular, the diagonals bisect each other, and not all four sides are congruent.
4 8. Quadrilateral ABCD is a parallelogram, a rectangle, a rhombus, and a square. Justification: opposite sides are parallel, consecutive sides are perpendicular, the diagonals bisect each other, and all four sides are congruent. 5B.3 answers: WB: Pgs Each beam. 9. The tree is 22.5 feet tall; Pgs Approximately Approximately 25.1 feet 10. RB: Pgs The object is miles deep; 9. Distance ; Pgs Approximately meters 10. 5B.4 answers: WB: Pgs cost =3/5=0.6; tant = 4/3 = sin A = 60/ ; cos A = 11/ ft ft The triangle is isosceles right and by definition its acute angles are AC = ; BC = ; m A=32
5 9. m X 48 ; m Z 42 ; YZ = in ft Pgs csc E = 25/ ; sec E = 25/ ; cot E = 24/ ft; 29 RB: Pgs. U ft ft Additional Problems: B.5 answers: WB: Pgs ft ft ,361 ft ft ; 48 Pgs ½. 5/13 4. ; ; 5. ; ; 6. cos 3 θ 8. 4/5 RB: Pgs. U θ 7. tan 2 θ or cotθ Unit 5B Test Review Key Yes 6. Yes 7. Yes 8. A. No, because both pairs of opposite sides are not parallel D. All of the above 11. A. Rhombus
6 12. Distance miles; feet from the base of the tree to the base of the shed. 15. is 3 inches X is 37 Z is feet 18. The distance between the ship and the submarine is 721 meters. The angle of depression of the naval ship is The building is 67 feet tall. 20. a. angle of depression b. angle of elevation c. angle of depression d. angle of elevation 21. sinθ = 22. cosθ = 0.98
7 Name: Date: Period: For Questions 1-4, NO CALCULATOR! Unit 5B Test Review Use for questions 1-2. Round your answers to the nearest thousandths. 1. Set up and calculate the trigonometric ratios for the sine, cosine, and tangent of. 2. Set up and calculate the trigonometric ratios for the cosecant, secant, and cotangent of. 3. Find the cosine of the complementary angle if 4. Find a value for for which is true.
8 Name: Date: Period: For Questions 5-22, you MAY use a calculator. 5. Use slope to determine whether the given vertices form a parallelogram: A(-8,-7), B(-6,-2), C(2,-2), D(0,-7) 6. Use the distance formula to determine whether the given vertices form a parallelogram: A(-1,1), B(5,1), C(2,-3), D(-4,-3) 7. Use the midpoint formula to determine whether the given vertices form a parallelogram: A(-8,-7), B(-6,-2), C(2,-2), D(0,-7) 8. Determine whether these four vertices form a parallelogram: A(-5,2), B(-2,-3), C(8,3), D(5,-8) a. No, because both pairs of opposite sides are not parallel. b. Yes, because both pairs of opposite sides are parallel. c. No, because the diagonals bisect each other. d. Yes, because the diagonals bisect each other.
9 9. Solve for the variables: 10. If the diagonals of a given quadrilateral are perpendicular, how could the quadrilateral be classified? a. Rhombus b. Square c. Kite d. All of the above 11. Classify a quadrilateral as precisely as possible given four vertices: E (0, 1), F (3, 5), G ( 2, 5), and H ( 5, 1). a. Rhombus b. Square c. Kite d. All of the above 12. A surveyor is mapping a large marsh in a state park. He walks and measures a straight line south from a cliff for 0.75 mile to a large tree. He walks east, but he has to make a detour around the marsh. He gets around the marsh to a spot where he is perpendicular to the large tree and the trail he originally walked south on. He looks northwest and measures a angle northwest to the cliff from his line of sight to the large tree. He measures the distance back to the cliff as 1.17 miles. What is the straight-line distance from the large tree east to? What is the tangent of? 13. What is the value of y? Round to the nearest whole number.
10 14. A recent storm downed a tree in your backyard. The top of the tree is now leaning on the roof of your shed. The shed s roof is 8 feet tall and the tree is 10 feet long. The angle that the tree makes with the ground is θ. a. How far is the base of the tree from the base of the shed? b. Find the measure of angle θ. Round to the nearest whole number. 15. Solve the right triangle XYZ, where Y is a right angle,, and. Find the missing angles and side lengths. Round to the nearest whole number. 16. What is the value of x? Round to the nearest whole number. 17. You are standing on a riverbank. An observation tower on the other side of the river is known to be 125 feet tall. An imaginary line from the top of the observation tower to your feet makes an angle of 16 with the ground. How far away are you from the base of the tower? Round to the nearest whole number.
11 18. A naval ship is stationed in calm waters. The sonar detects a submarine at a depth of about 400 meters and a horizontal distance of 600 meters. What is the distance between the ship and the submarine? What is the angle of depression of the naval ship? Round both answers to the nearest whole number. 19. A 5-foot-tall woman is standing 67 feet from a building. When she looks at the top of the building the angle of elevation is 43. Find the height of the building to the nearest foot. 20. State whether the angle is an angle of depression or elevation in the picture below. a. b. c. d. 21. Find sinθ if 0 < θ < 90 and cosθ =. Find the value using the Pythagorean Identity, leave in fraction form. 22. The incline of a road going up a hill is θ. The length of the road going up the hill is 150 meters, and the vertical rise of the hill is 30 meters. Find cosθ. Round to the nearest hundredth place.
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