Name: Class: Date: Chapter 3 - Foundations 7. Multiple Choice Identify the choice that best completes the statement or answers the question.

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1 Name: Class: Date: Chapter 3 - Foundations 7 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the value of tan 59, to four decimal places. a c b d In ABC, AB = 15 cm and AC = 9 cm. Determine the tangent ratio of B, to the nearest hundredth. a c b d In the triangle, AC = 9 cm and tan B = What is the length of BC? a. 8 cm c. 12 cm b. 10 cm d. 15 cm 4. Determine the measure of C, to the nearest degree. a. 19 c. 21 b. 20 d The ratio of vertical distance to horizontal distance for a flight of steps is 3m to 4m. Determine the angle that the steps make with the ground, to the nearest degree. a. 23 c. 75 b. 37 d

2 Name: Use the diagram to answer the following question(s). 6. Determine the length of x, to the nearest tenth of a metre. a. 5.7 m c. 7.0 m b. 6.3 m d. 8.2 m 7. Determine the length of y, to the nearest tenth of a metre. a. 5.7 m c. 7.0 m b. 6.3 m d. 8.2 m 8. A cone just fits inside a can. The diameter of the can is 7.6 cm and the height is 10.4 cm. Determine the angle between the vertex of the cone and the bottom of the can, to the nearest tenth of a degree. a c b d In a right triangle, sin B = Determine the measure of B, to the nearest degree. a. 73 c. 17 b. 18 d. 1 2

3 Name: 10. In ABC, AC = 8 cm and BC = 11 cm. Determine the sine ratio of B, rounded to the nearest thousandth. a c b d Write the cosine ratio of A. a. b. AB AC BC AB c. d. AC BC BC AC 12. In the triangle, AC = 26 cm and AB = 10 cm. Determine the sine ratio of A, to the nearest thousandth. a c b d

4 Name: 13. In ABC, BC = 48 cm and sin A = Determine the length of AC, to the nearest centimetre. a. 14 cm c. 25 cm b. 24 cm d. 50 cm 14. Evaluate sin 90. a. 1 c. 1 b. 0 d. undefined 15. Determine the measure of F, to the nearest degree. a. 36 c. 38 b. 37 d. 39 4

5 Name: Use the diagram to answer the following question(s). Kelly is flying a kite in a field. He lets out 40 m of his kite string, which makes an angle of 72 with the ground. 16. Suppose the sun is shining directly above the kite. How far is the kite s shadow from Kelly, to the nearest metre? a. 12 m c. 42 m b. 38 m d. 129 m 17. Determine the length of x and the length of y, to the nearest tenth of a metre. a. x = 7.2 m and y = 9.7 m c. x = 9.6 m and y = 14.3 m b. x = 9.6 m and y = 12.9 m d. x = 7.2 m and y = 10.8 m 18. The length of side x, to the nearest tenth of a metre, is a m c m b m d m 5

6 Name: Problem 1. A cell phone tower is supported by two guy wires, attached on opposite sides of the tower. One guy wire is attached to the top of the base of the tower at point A. The other is attached to the base at point E, at a height of 70 m above the ground. a) Demonstrate that ABC and EBD are similar triangles. b) Determine the height of the base of the tower, to the nearest metre. c) Determine the length of each guy-wire, to the nearest metre. 2. José is sitting in a tree, so that his eyes are 3.2 m above the ground. When he looks down at an angle of depression of 43, he can see his cat sitting in the yard. a) Draw a diagram of the situation. b) Determine the horizontal distance, to the nearest tenth of a metre, from the base of the tree to José s cat. 6

7 Name: 3. Tim lives on Taylor Avenue, 500 m west of where it intersects with Swift Street. The library is on Swift Street, north of the intersection. a) When Tim goes from his house to the library, he walks diagonally across a field at an angle of 30 to Taylor Avenue. How far does Tim walk if he takes this route? Answer to the nearest tenth of a metre. b) If Tim decides to walk from his house to the library along the streets, how far does he travel? Answer to the nearest tenth of a metre. c) Determine which route is shorter, and by how much. 4. Max s dog is lying on the ground 1.2 m away from him. The angle of elevation from the dog to the top of Max s head is 48. How tall is Max, to the nearest tenth of a metre? 5. The string on Yuri s kite is 45 m long and makes an angle of 55 with the ground. Yuri s friend, Abdul, is standing directly below the kite. a) How far apart are Abdul and Yuri now, to the nearest tenth of a metre? b) Abdul runs away from Yuri, so that the angle of elevation between Abdul and the kite is 15. How far apart are Abdul and Yuri, to the nearest tenth of a metre? 7

8 Chapter 3 - Foundations 7 Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: B OBJ: Section 3.1 NAT: M4 TOP: The Tangent Ratio KEY: tangent ratio calculate a tangent ratio 2. ANS: B PTS: 1 DIF: B OBJ: Section 3.1 NAT: M4 TOP: The Tangent Ratio KEY: tangent ratio calculate a tangent ratio right triangle 3. ANS: C PTS: 1 DIF: B OBJ: Section 3.1 NAT: M4 TOP: The Tangent Ratio KEY: tangent ratio determine a distance using trigonometry right triangle 4. ANS: C PTS: 1 DIF: B OBJ: Section 3.1 NAT: M4 TOP: The Tangent Ratio KEY: tangent ratio determine an angle measure right triangle 5. ANS: B PTS: 1 DIF: B OBJ: Section 3.3 NAT: M4 TOP: Solving Right Triangles KEY: tangent ratio determine an angle measure 6. ANS: C PTS: 1 DIF: C OBJ: Section 3.1 NAT: M4 TOP: The Tangent Ratio KEY: tangent ratio determine a distance using trigonometry 7. ANS: B PTS: 1 DIF: C OBJ: Section 3.1 NAT: M4 TOP: The Tangent Ratio KEY: tangent ratio determine a distance using trigonometry 8. ANS: C PTS: 1 DIF: D OBJ: Section 3.3 NAT: M4 TOP: Solving Right Triangles KEY: tangent ratio determine an angle measure 9. ANS: C PTS: 1 DIF: B OBJ: Section 3.2 KEY: sine ratio determine an angle measure 10. ANS: A PTS: 1 DIF: B OBJ: Section 3.2 KEY: sine ratio calculate a sine ratio right triangle 11. ANS: A PTS: 1 DIF: A OBJ: Section 3.2 KEY: cosine ratio write a cosine ratio right triangle 12. ANS: C PTS: 1 DIF: B OBJ: Section 3.2 KEY: sine ratio calculate a sine ratio right triangle 13. ANS: A PTS: 1 DIF: B OBJ: Section 3.2 KEY: sine ratio determine a distance using trigonometry right triangle 14. ANS: C PTS: 1 DIF: A OBJ: Section 3.2 KEY: sine ratio calculate a sine ratio 1

9 15. ANS: B PTS: 1 DIF: B OBJ: Section 3.2 KEY: cosine ratio determine an angle measure 16. ANS: A PTS: 1 DIF: C OBJ: Section 3.3 NAT: M4 TOP: Solving Right Triangles KEY: cosine ratio determine a distance using trigonometry solve a right triangle 17. ANS: D PTS: 1 DIF: C OBJ: Section 3.2 KEY: sine ratio determine a distance using trigonometry right triangle 18. ANS: B PTS: 1 DIF: A OBJ: Section 3.3 NAT: M4 TOP: Solving Right Triangles KEY: Pythagorean theorem right triangle 2

10 PROBLEM 1. ANS: a) C D 70 ; ABC EBD 90 ; A E 20 AC corresponds to ED, BC corresponds to BD, and AB corresponds to EB, so the triangles are similar. height of tower b) tanc distance of wire to base of tower tan 70 AB 42 42(tan70 ) AB AB The base of the tower is approximately 115 m tall. c) cosc cos AC AC distance from wire to base of tower length of wire 42 cos70 AC The guy wire attached to the top of the base of the tower is approximately 123 m long. height of tower sind length of wire sin ED ED 70 sin70 ED The second guy wire is approximately 74 m long. PTS: 1 DIF: C OBJ: Section 3.3 NAT: M4 TOP: Solving Right Triangles KEY: tangent ratio sine ratio cosine ratio solve a right triangle similar triangles 3

11 2. ANS: a) Example: b) Let d represent the distance from the cat to the base of the tree, in metres. distance from base of tree to cat tan43 height of Jose above the ground tan43 d (tan43 ) d d The distance from the base of the tree to the cat is about 3.0 m. PTS: 1 DIF: A OBJ: Section 3.3 NAT: M4 TOP: Solving Right Triangles KEY: tangent ratio determine a distance using an angle of depression 4

12 3. ANS: a) Let d represent the diagonal distance across the field, in metres. distance from Tim's house to Swift Street cos30 diagonal distance through field cos d d 500 cos30 d If Tim takes the route through the field, he walks m. b) Let x the distance of the library from the intersection. distance of library from intersection tan30 distance of house from intersection tan30 x (tan30 ) x x Total distance = distance from house to intersection + distance from intersection to library Total distance = Total distance = If Tim walks along the streets, he walks approximately m. c) = The route through the field is m shorter than the route along the streets. PTS: 1 DIF: C OBJ: Section 3.3 NAT: M4 TOP: Solving Right Triangles KEY: cosine ratio determine a distance using trigonometry 4. ANS: Let h represent Max s height, in metres. tan48 tan48 h (tan48 ) h h Max is about 1.3 m tall. height of Max distance from Max to dog PTS: 1 DIF: A OBJ: Section 3.3 NAT: M4 TOP: Solving Right Triangles KEY: tangent ratio determine a distance using an angle of elevation determine a distance using trigonometry 5

13 5. ANS: a) Let x represent the distance between Abdul and Yuri, in metres. distance between Abdul and Yuri cos55 length of kite string cos 55 x 45 45(cos 55 ) x x Abdul and Yuri are approximately 25.8 m apart. b) Let h represent the height of the kite above the ground, in metres. height of the kite above the ground sin55 length of kite string sin55 h 45 45(sin55 ) h h Let x represent the horizontal distance between Abdul and the kite, in metres. height of the kite above the ground tan15 horizontal distance between Abdul and the kite tan x x 36.9 tan15 x Distance between Abdul and Yuri = = The distance between Abdul and Yuri is now approximately m. PTS: 1 DIF: D OBJ: Section 3.2 NAT: M4 TOP: The Sine and Cosine Ratios KEY: cosine ratio determine a distance using trigonometry angle of elevation solve a right triangle 6

Name: Block: What I can do for this unit:

Unit 8: Trigonometry Student Tracking Sheet Math 10 Common Name: Block: What I can do for this unit: After Practice After Review How I Did 8-1 I can use and understand triangle similarity and the Pythagorean