ath 1201 hapter 2 Review ultiple hoice Identify the choice that best completes the statement or answers the question. 1. etermine tan and tan. 8 10 a. tan = 1.25; tan = 0.8 c. tan = 0.8; tan = 1.25 b. tan = 0.8; tan = 0.7809... d. tan = 0.6247...; tan = 1.25 2. etermine the measure of to the nearest tenth of a degree. 9 E 3 F a. 18.4 b. 19.5 c. 70.5 d. 71.6 3. etermine the angle of inclination of the line to the nearest tenth of a degree. 4.4 9.8 a. 63.3 b. 24.2 c. 65.8 d. 26.7 4. etermine the measure of to the nearest tenth of a degree. 8 cm 19 cm a. 65.1 b. 67.2 c. 22.8 d. 24.9 5. ladder leans against the side of a building. The top of the ladder is 5 m from the ground. The base of the ladder is 1.0 m from the wall. What angle, to the nearest degree, does the ladder make with the ground? a. 79 b. 11 c. 9 d. 83 6. etermine the tangent ratio for K. 12 37 K a. 12 35 b. 12 37 c. 37 12 d. 35 12 June 2014 1
7. etermine the length of side z to the nearest tenth of a centimetre. X 4.7 cm 61 Z z Y a. 9.7 cm b. 2.6 cm c. 5.4 cm d. 8.5 cm 8. etermine sin and cos to the nearest tenth. 20 12 16 a. sin = 1.7; cos = 0.8 c. sin = 0.6; cos = 1.3 b. sin = 0.8; cos = 0.6 d. sin = 0.6; cos = 0.8 9. etermine the measure of to the nearest tenth of a degree. E 21 8 F a. 67.6 b. 69.1 c. 22.4 d. 20.9 10. etermine the measure of Q to the nearest tenth of a degree. P 7 Q 19 R a. 68.4 b. 69.8 c. 21.6 d. 20.2 11. helicopter is hovering 200 m above a road. car stopped on the side of the road is 300 m from the helicopter. What is the angle of elevation of the helicopter measured from the car, to the nearest degree? a. 56 b. 48 c. 42 d. 34 June 2014 2
12. etermine the measure of to the nearest tenth of a degree. 25 17 a. 94.3 b. 34.2 c. 42.8 d. 47.2 13. etermine the length of N to the nearest tenth of an centimetre. 18.8 cm 63 N a. 36.9 cm b. 41.4 cm c. 8.5 cm d. 16.8 cm 14. etermine the length of XY to the nearest tenth of a centimetre. Y X 61 17.4 cm Z a. 8.4 cm b. 15.2 cm c. 31.4 cm d. 19.9 cm 15. etermine the length of RS to the nearest tenth of a metre. R T 18.8 m 17 S a. 19.7 m b. 5.7 m c. 18.0 m d. 64.3 m 16. etermine the length of E to the nearest tenth of a centimetre. 7.7 cm E 29 F a. 8.8 cm b. 15.9 cm c. 3.7 cm d. 13.9 cm June 2014 3
17. Solve this right triangle. Give the measures to the nearest tenth. U 6.5.0 cm V 13.0 cm W a. cm c. cm b. cm d. cm 18. n architect draws this diagram of a wheelchair entrance ramp for a building. etermine the angle of inclination of the ramp to the nearest tenth of a degree. 7.0 m 0.4 m a. 86.7 b. 29.7 c. 3.3 d. 5.1 19. etermine the length of this wheelchair ramp to the nearest hundredth of a metre. 4.50 m 0.60 m a. 4.60 m b. 7.50 m c. 4.46 m d. 4.54 m 20. etermine the area of to the nearest square centimetre. R T 23.3 cm 21 S a. 291 cm 2 b. 707 cm 2 c. 104 cm 2 d. 208 cm 2 21. etermine the perimeter of an equilateral triangle with height 11.9 cm. Give the measure to the nearest tenth of a centimetre. a. 81.8 cm b. 41.2 cm c. 30.9 cm d. 71.4 cm 22. etermine the length of N to the nearest tenth of a centimetre. K 49 8.2 cm 33 N a. cm b. cm c. cm d. cm June 2014 4
Short nswer 23. Tan = 1.3; determine the measure of to the nearest tenth of a degree. 24. a) For in the triangle below, label the hypotenuse and the opposite and adjacent sides. b) etermine tan to the nearest hundredth. 16 65 K 25. The base of a ladder is 0.6 m from a wall of a house. The top of the ladder rests against the house 2.0 m above the ground. etermine the angle the ladder makes with the house, to the nearest degree. 26. etermine the length of side r to the nearest tenth of a metre. R 28 23.1 m S r T 27. Solve this right triangle. Give the measures to the nearest tenth. 19.9 cm 57 N 28. Solve this right triangle. Give the measures to the nearest tenth. 9.1 cm F 26 E 29. etermine the length of WX to the nearest tenth of a centimetre. W 9.5 cm 29 Z X 31 Y June 2014 5
Problem 30. etermine the measures of and to the nearest tenth of a degree. 3 4 31. guy wire is connected from a tower to the ground. etermine the height of the tower, to the nearest tenth of a metre. What assumptions about the ground are you making? 32. etermine the area of to the nearest tenth of a square unit. etermine its perimeter to the nearest tenth of a unit. 57 23.6 33. etermine the measures of and to the nearest tenth of a degree. 23 11 34. etermine the area of this right triangle to the nearest square metre. 850 m 57 N June 2014 6
35. etermine the perimeter of this triangle to the nearest tenth of a centimetre. \ 9.0 cm / 34 36. Solve N. Give the measures to the nearest tenth. Explain your strategy. 4.8 cm 8.1 cm N 37. Solve XYZ. Give the measures to the nearest tenth. Explain your strategy. X Y 18.9 cm 45 Z 38. In this regular hexagon, the distance from one vertex to the opposite vertex, measured through the centre of the hexagon, is approximately 15.0 cm. etermine the perimeter of the hexagon to the nearest tenth of a centimetre. 15.0 cm June 2014 7
39. Girl Guide measured the angle of elevation of the top of a monument as 59. The height of the monument is 38.5 m. She then walked 31.0 m due west from the point where she measured the angle of elevation. etermine the angle of elevation of the monument from her new location to the nearest tenth of a degree. 38.5 m 31.0 m 59 nswer Section UTIPE HOIE 1. NS: 2. NS: 3. NS: 4. NS: 5. NS: 6. NS: 7. NS: 8. NS: 9. NS: 10. NS: 11. NS: 12. NS: 13. NS: 14. NS: 15. NS: 16. NS: 17. NS: 18. NS: 19. NS: 20. NS: 21. NS: 22. NS: SHORT NSWER 23. NS: 52.4 24. NS: a) adjacent opposite hypotenuse K b) tan = 0.25 25. NS: 17 26. NS: 12.3 m 27. NS: N = 10.8 cm = 16.7 cm = 33.0 28. NS: EF = 18.7 cm F = 20.8 cm = 64.0 29. NS: 16.1 cm June 2014 8
PROE 30. NS: etermine the measure of in right. etermine the measure of. 31. NS: In right E, side E is opposite and E is adjacent to. Solve the equation for E. The height of the tower is approximately 26.2 m. I am assuming the ground is horizontal. 32. NS: etermine the length of. In right, is opposite and is adjacent to. Solve the equation for. Find the area of. June 2014 9
The area of is approximately 428.8 square units. etermine the length of. Use the Pythagorean Theorem in right. The perimeter of is: The perimeter of is approximately 103.3 units. 33. NS: etermine the measure of In right : first. is approximately 61.4 and is approximately 28.6. 34. NS: In right N, N is the hypotenuse, is opposite N, and N is adjacent to N. Use the sine ratio to determine the height of the triangle,. Solve this equation for. Use the cosine ratio to determine the length of N, the base of the triangle. June 2014 10
Solve this equation for N. Use the formula for the area,, of a triangle. The area of the triangle is approximately 165 009 m. 35. NS: In right, is the hypotenuse, is opposite, and is adjacent to. To determine the length of, use the sine ratio. Solve this equation for. To determine the length of, use the cosine ratio. Solve this equation for. June 2014 11
Since = and =, the perimeter, P, of the triangle is: Τhe perimeter of the triangle is approximately 58.9 cm. 36. NS: etermine the length of first. Use the Pythagorean Theorem in right N. is approximately 6.5 cm. etermine the measure of N. Since N is adjacent to N and N is the hypotenuse, use the cosine ratio. N is approximately 53.7 and is approximately 36.3. 37. NS: The acute angles in a right triangle have a sum of 90. In right XYZ: etermine the length of XY. Since XY is opposite Z and YZ is adjacent to Z, use the tangent ratio. XY is approximately 18.9 cm. etermine the length of XZ. Since YZ is adjacent to Z and XZ is the hypotenuse, use the cosine ratio. June 2014 12
XZ is approximately 26.7 cm. 38. NS: ongruent isosceles triangles are formed by drawing line segments from the centre of the hexagon to each vertex. In each triangle, the angle at the centre is: 7.5 cm The line segment from the centre of the hexagon to the centre of each side of the hexagon bisects each central angle and is perpendicular to the side. So, in right, 30 60 7.5 cm 7.5 cm Since, then, and nd, the perimeter of the hexagon is: The perimeter of the hexagon is approximately 45.0 cm. 39. NS: abel a diagram. Use right to calculate the length of. is opposite and is adjacent to. So, use the tangent ratio. 38.5 m 31.0 m 59 Use right to calculate the measure of. First determine the length of. June 2014 13
etermine the measure of. is opposite and is adjacent to. So, use the tangent ratio. Τhe angle of elevation of the monument from the new location is approximately 35.4. June 2014 14