Chapter 8 Diagnostic Test

Transcription

1 Chapter 8 Diagnostic Test STUDENT BOOK PAGES Determine the measures of the indicated angles in each diagram. b) 2. Determine the value of each trigonometric ratio to four decimal places. sin 33º b) cos 27º c) cos 75º d) sin 68º 3. Determine the measure of A to the nearest degree. sin A = c) sin A = b) cos A = d) cos A = Solve. x 15 8 = b) = x 12 c) d) 14 9 = 7 x 18 x = Determine the value of x in each triangle. Round your answers to one decimal place. b) c) Chapter 8 Diagnostic Test 445

2 Chapter 8 Diagnostic Test Answers 1. a = 50º, b = 65º, c = 115º b) d = 52º, e = 45º, f = 83º b) c) d) º b) 30º c) 58º d) 33º b) 9 c) 4.5 d) º b) 36.9º c) 23.0 cm If students have difficulty with the questions in the Diagnostic Test, it may be necessary to review the following topics: applying properties of angles in a triangle and angles formed by parallel lines to determine angle measures solving proportions determining and using the primary trigonometric ratios applying the primary trigonometric ratios to determine side lengths and angle measures 446 Principles of Mathematics 10: Chapter 8 Diagnostic Test Answers

3 Lesson 8.2 Extra Practice STUDENT BOOK PAGES Solve. Determine x to one decimal place and θ to the nearest degree. x 7.5 = sin 43 sin 71 sin 61 sin 65 b) = x 31 sin 55 sinθ c) = sin θ sin 73 d) = Solve each triangle. b) 2. Determine the indicated side lengths and angle measures. b) 5. Solve each triangle. Determine each side length to one decimal place and each angle measure to the nearest degree. In+ABC, B = 42º, C = 59º, and a = 20.0 cm. b) In+RST, r = 15 cm, s = 12 cm, and S = 48º. 6. Three towns, represented by points A, B, and C, are located so that B is 25.0 km from A, and C is 34.4 km from A. If B = 80º, determine the distance from B to C. 3. In+ABC, a = 22 cm, B = 53º, and C = 43º. Determine the length of side b. b) In+PQR, q = 9 cm, r = 7 cm, and R = 47º. Determine the measure of Q. Lesson 8.2 Extra Practice 447

4 Lesson 8.2 Extra Practice Answers b) 29.9 c) 72º d) 47º 2. about 18.2 cm b) about 62º 3. about 18 cm b) about 70º 4. A = 35º, a = 7 cm, c = 10 cm b) P = 56º, Q = 44º, p = 421 m 5. A = 79º, b = 13.6 cm, c = 17.5 cm b) R = 68º, T = 64º, t = 14.5 cm 6. about 28.3 km 448 Principles of Mathematics 10: Lesson 8.2 Extra Practice Answers

5 Chapter 8 Mid-Chapter Review Extra Practice STUDENT BOOK PAGES Determine the indicated side lengths to one decimal place and the indicated angle measures to the nearest degree. b) 2. Write three equivalent ratios using the sides and angles in acute triangle KLM. Record the answer in two different ways. 3. In+ABC, A = 47º, B = 65º, and b = 6.8 cm. Determine the length of side a. b) In+DEF, E = 59º, F = 41º, and d = 93 cm. Determine the length of side f. c) In+PQR, Q = 70º, p = 5 cm, and q = 7 cm. Determine the measure of P. 4. Solve each triangle. In+PQR, P = 70º, R = 25º, and q = 55 cm. b) In+DEF, E = 50º, e = 33 cm, and f = 41 cm. 5. In+ABC, c = 45.0 cm, A = 70º, and B = 60º. Determine the perimeter of+abc. c) 6. A slide in a park is 9 m long, and its ladder is 7 m long. If the slide makes an angle of 48º with the ground, determine the angle that the ladder makes with the ground. 7. Two points, A and B, are located on opposite sides of a river. Point C is located 125 m from point B, on the same side of the river. If ABC = 71º and ACB = 47º, determine the distance from A to B. d) Chapter 8 Mid-Chapter Review Extra Practice 449

6 Chapter 8 Mid-Chapter Review Extra Practice Answers 1. b = 22.7 cm b) a = 18.6 cm, b = 22.2 cm c) θ = 39º d) θ = 60º, α = 52º 2. k sin K sin K k l = sin L sin L = l = = m sin M sin M m 3. about 5.5 cm b) about 62 cm c) about 42º 4. Q = 85º, p = 52 cm, r = 23 cm b) D = 58º, F = 72, d = 37 cm 5. about cm 6. about 73º 7. about 104 m 450 Principles of Mathematics 10: Chapter 8 Mid-Chapter Review Extra Practice Answers

7 Lesson 8.4 Extra Practice STUDENT BOOK PAGES Record the cosine law for+jkl for determining the length of side j. b) Record the cosine law for+str for determining the measure of R. 2. Determine the length of each indicated side. b) 3. Determine the measure of each indicated angle. 4. Correct the mistake(s) in each of these for acute triangle XYZ. y 2 = x 2 + z 2 2 xy cos Y b) x 2 = y 2 + z 2 yz cos X c) z 2 = x 2 + z xy cos Z d) y 2 = x 2 + y 2 2 xy cos Y e) z 2 = x 2 + y 2 + xy cos Y 5. Solve each triangle. In+ABC, B = 43º, a = 10.5 m, c = 11.2 m. b) In+DEF, d = 60 m, e = 50 m, f = 40 m. c) In+PQR, p = 10.0 m, r = 15.0 m, Q = 50º. 6. Determine the perimeter of+abc if a = 43.0 cm, b = 28.0 cm, and C = A parallelogram has sides that are 12.0 cm and 18.0 cm long. The angle between these sides is 78º. Determine the length of the shorter diagonal. 8. A jogger travels 5.4 km directly east, and then turns and travels 6.3 km in a N57ºW direction. How far does the jogger have to travel to go directly back to the starting point? b) Lesson 8.4 Extra Practice 451

8 Lesson 8.4 Extra Practice Answers 1. j 2 = k 2 + l 2 2 kl cos J b) r 2 = s 2 + t 2 2 st cos R 2. about 6.2 cm b) about 6.8 cm 3. about 55º b) about 63º 4. y 2 = x 2 + z 2 2 xz cos Y b) x 2 = y 2 + z 2 2 yz cos X c) z 2 = x 2 + y 2 2 xy cos Z d) y 2 = x 2 + z 2 2 xz cos Y e) z 2 = x 2 + y 2 2 xy cos Z 5. b = 8.0 m, A = 64º, C = 73º b) D = 83º, E = 56º, F = 41º c) q = 11.5 m, P = 42º, R = 88º 6. about cm 7. about 19.4 cm 8. about 3.4 km 452 Principles of Mathematics 10: Lesson 8.4 Extra Practice Answers

9 Lesson 8.5 Extra Practice STUDENT BOOK PAGES Would you use the sine law or the cosine law for each of the following? The length of each side is given, and you need to determine the measure of an angle. b) The lengths of two sides and the angle opposite one of the sides are given, and you need to determine the measure of an angle. c) The lengths of two sides and the contained angle are given, and you need to determine the length of the other side. 2. In+ABC, AB = 30.0 cm, A = 80º, and B = 55º. Determine the perimeter of+abc. 3. An isosceles triangle has sides that are 4 cm, 10 cm, and 10 cm long. Determine the measure of the equal angles. 4. Louise works for a landscaping company. Her job involves measuring properties that are going to be landscaped. A triangular property has a 4.9 m side and a 5.8 m side, which meet at a 35º angle. Determine the perimeter of the property. 5. A surveyor is locating three points, M, N, and P, around an artificial pond. The distance from M to N is 728 m, and the distance from M to P is 638 m. The measure of N is 57º. Determine the measure of M. b) Determine the distance from N to P. 6. The buoys that mark a triangular course for a yacht race are located at points Y, T, and B. If YT = 5.5 km, Y = 55º, and T = 75º, determine the length of the course. 7. Todd and Scott leave the dining hall at a camp. They walk on two straight paths that diverge by 48º. Scott walks 580 m, and Todd walks 740 m. How far apart are they? 8. Two fishing boats leave the same dock at the same time. One boat travels at a speed of 15.0 km/h, and the other boat travels at a speed of 18.0 km/h. After 45 min, the boats are 14.0 km apart. Assuming that both boats are travelling in straight paths, what is the angle between their paths? Lesson 8.5 Extra Practice 453

10 Lesson 8.5 Extra Practice Answers 1. cosine law b) sine law c) cosine law 2. about cm 3. about 78º 4. about 14.0 m 5. about 50º b) about 583 m 6. about 18.3 km 7. about 556 m 8. about 68º 454 Principles of Mathematics 10: Lesson 8.5 Extra Practice Answers

11 Chapter 8 Review Extra Practice STUDENT BOOK PAGES Which of the following are not correct for acute triangle RST? s t = sin S sint sin R sint b) = r s sin S t c) = s sint d) s sin S = t sin T e) r sin T = t sin R 5. Calculate the indicated side length or angle measure in each triangle. b) 2. Calculate the indicated side length or angle measure in each triangle. 6. Solve+DEF, if d = 9 cm, e = 7 cm, and f = 10 cm. b) 7. Two planes are flying at the same altitude. They are 3000 m apart when they spot a raft on the sea below them. The angles of depression to the raft are 57º and 48º. Determine the distance from the raft to the closer plane. 8. A plot of land is the shape of an isosceles triangle, with equal sides that are 175 m long. The angle between the equal sides is 80º. Determine the length of the third side. 3. Solve+ABC, if A = 32º, B = 72º, and b = 72.4 cm. 4. Akila is making a triangular support to hang plants. She is using three lengths of pipe, which measure 34 cm, 25 cm, and 28 cm. Determine the angles in the triangular support. 9. A parallelogram has adjacent sides that are 12 cm and 18 cm long. The shorter diagonal is 15 cm long. Determine the measures of all four angles in the parallelogram. Chapter 8 Review Extra Practice 455

12 Chapter 8 Review Extra Practice Answers 1. b), c), d) 2. b = 29 cm, c = 32 cm b) θ = 46º, α = 59º 3. C = 76º, a = 40.3 cm, c = 73.9 cm 4. about 54º, about 80º, about 46º 5. about 7.3 cm b) about 76º 6. D = 61º, E = 43º, F = 76º 7. about 2308 m 8. about 225 m 9. about 56º, about 124º, about 56º, about 124º 456 Principles of Mathematics 10: Chapter 8 Review Extra Practice Answers

13 Chapters 7 8 Cumulative Review Extra Practice STUDENT BOOK PAGES What is the value of x? 5. What is the length of side a? A cm B. 5.1 cm C. 7.1 cm D. 9.4 cm 2. A board that is 3.2 m long is leaning against a vertical wall, with its foot 2.0 m away from the wall. Another board, which is 4.8 m long, is leaning against the wall, parallel to the first board. How far is the foot of the second board from the wall? A. 1.0 m B. 4.0 m C. 4.8 m D. 3.0 m A m B m C m D. 7.2 m 6. In+ABC, A = 47º, b = 20.0 cm, and c = 14.0 cm. What is the length of side a? A cm B cm C cm D cm 7. What is the measure of θ? 3. What is the value of θ to the nearest degree? A. 50º B. 40º C. 56º D. 35º 4. John is standing at the top of a hill. He observes that the angle of depression to the bottom of the hill is 40º. If the distance to walk down the hill is 15 m, what is the vertical distance from the top of the hill to the ground? A m B m C. 7.5 m D. 9.6 m A. 72º B. 31º C. 58º D. 70º 8. In+ABC, A = 80º, B = 40º, and a = 7.5 cm. Solve+ABC. A. b = 4.9 cm, c = 6.6 cm, C = 40º B. b = 6.6 cm, c = 4.9 cm, C = 60º C. b = 4.9 cm, c = 6.6 cm, C = 60º D. b = 3.6 cm, c = 11.3 cm, C = 40º 9. In+DEF, d = 4.6 m, e = 4.2 m, and f = 2.1 m. Solve+DEF. A. D = 86º, E = 34º, F = 60º B. D = 87º, E = 66º, F = 27º C. D = 34º, E = 86º, F = 60º D. D = 65º, E = 88º, F = 27º Chapters 7 8 Cumulative Review Extra Practice 457

14 Chapters 7 8 Cumulative Review Extra Practice Answers 1. C 2. D 3. B 4. D 5. A 6. B 7. A 8. C 9. B 458 Principles of Mathematics 10: Chapters 7 8 Cumulative Review Extra Practice Answers