GEOM - Notre Dame Academy



GEOM. CH. 8 TRIGONOMETRY FUNCTIONS TEST PREVIEW

Multiple Choice

Identify the choice that best completes the statement or answers the question.

Find the length of the missing side. The triangle is not drawn to scale.

____ 1. [pic]

|a. |25 |b. |625 |c. |168 |d. |62 |

Find the length of the missing side. Leave your answer in simplest radical form.

____ 2. [pic]

|a. |[pic] cm |b. |109 cm |c. |[pic] cm |d. |[pic] cm |

____ 3. Wayne used the diagram to compute the distance from Ferris to Dunlap to Butte. How much shorter is the distance directly from Ferris to Butte than the distance Wayne found?

[pic]

|a. |20 mi |b. |25 mi |c. |10 mi |d. |35 mi |

____ 4. A triangle has sides of lengths 10, 24, and 26. Is it a right triangle? Explain.

|a. |yes; [pic] |c. |no; [pic] |

|b. |no; [pic] |d. |yes; [pic] |

____ 5. The figure is drawn on centimeter grid paper. Find the perimeter of the shaded figure to the nearest tenth.

[pic]

|a. |17.6 cm2 |b. |10.8 cm2 |c. |15.6 cm2 |d. |18.0 cm2 |

____ 6. Find the length of the hypotenuse.

[pic]

|a. |12 |b. |6 |c. |5 |d. |18 |

____ 7. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth.

[pic]

|a. |x = 9, y = 12.7 |b. |x = 6.4, y = 7.8 |c. |x = 12.7, y = 9 |d. |x = 7.8, y = 6.4 |

____ 8. The area of a square garden is 200 m2. How long is the diagonal?

|a. |20 m |b. |100 m |c. |400 m |d. |[pic] m |

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

____ 9. [pic]

Not drawn to scale

|a. |x = 33, y = [pic] |c. |x = [pic], y = [pic] |

|b. |x = [pic], y = 11 |d. |x = 11, y = [pic] |

____ 10. Find the value of x and y rounded to the nearest tenth.

[pic]

|a. |x = 48.1, y = 46.4 |c. |x = 24.0, y = 139.3 |

|b. |x = 48.1, y = 139.3 |d. |x = 24.0, y = 46.4 |

____ 11. A piece of art is in the shape of an equilateral triangle with sides of 17 in. Find the area of the piece of art. Round your answer to the nearest tenth.

|a. |125.1 in.2 |b. |250.3 in.2 |c. |none of these |d. |102.2 in.2 |

____ 12. A conveyor belt carries supplies from the first floor to the second floor, which is 25 feet higher. The belt makes a 60° angle with the ground.

a. How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot.

b. If the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to the second floor?

|a. |14 ft; 1 min |b. |35 ft; 21.8 min |c. |43 ft; 36 min |d. |29 ft; 0.4 min |

____ 13. Write the tangent ratios for [pic] and [pic].

[pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

Find the value of x. Round your answer to the nearest tenth.

____ 14. [pic]

|a. |3.4 |b. |27.5 |c. |3.6 |d. |9.4 |

Find the value of x to the nearest degree.

____ 15. [pic]

|a. |56 |b. |81 |c. |34 |d. |63 |

____ 16. The students in Mr. Collin’s class used a surveyor’s measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building.

[pic]

|a. |2400 ft |b. |72 ft |c. |308 ft |d. |33 ft |

____ 17. Find the value of w, then x. Round lengths of segments to the nearest tenth.

[pic]

|a. |w = 13.3, x = 10.2 |c. |w = 13.3, x = 23.6 |

|b. |w = 10.8, x = 6.1 |d. |w = 10.8, x = 16.9 |

____ 18. Write the ratios for sin A and cos A.

[pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

Find the value of x. Round to the nearest tenth.

____ 19. [pic]

|a. |14.8 |b. |17.3 |c. |17.7 |d. |15.2 |

____ 20. [pic]

|a. |5.3 |b. |5.1 |c. |43.9 |d. |44.2 |

Find the value of x. Round to the nearest degree.

____ 21. [pic]

|a. |32 |b. |39 |c. |51 |d. |38.5 |

____ 22. A slide 4.1 meters long makes an angle of 35[pic] with the ground. To the nearest tenth of a meter, how far above the ground is the top of the slide?

[pic]

|a. |7.1 m |b. |3.4 m |c. |5.0 m |d. |2.4 m |

____ 23. Find the value of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree.

[pic]

|a. |w = 7.7, x = 44 |c. |w = 7.7, x = 54 |

|b. |w = 6.4, x = 54 |d. |w = 6.4, x = 44 |

Find the value of x. Round the length to the nearest tenth.

____ 24. [pic]

|a. |55.6 m |b. |6.5 m |c. |6.9 m |d. |17.9 m |

____ 25. [pic]

|a. |877.1 m |b. |824.2 m |c. |102.6 m |d. |319.3 m |

____ 26. An airplane over the Pacific sights an atoll at an angle of depression of 5[pic]. At this time, the horizontal distance from the airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter?

[pic]

|a. |403 m |b. |405 m |c. |4611 m |d. |4647 m |

____ 27. To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44[pic]. To the nearest foot, what is the height of the pole?

|a. |145 ft |b. |149 ft |c. |135 ft |d. |139 ft |

____ 28. A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door?

|a. |39[pic] |b. |51[pic] |c. |53[pic] |d. |37[pic] |

GEOM. CH. 8 TRIGONOMETRY FUNCTIONS TEST PREVIEW

Answer Section

MULTIPLE CHOICE

1. ANS: A

2. ANS: D

3. ANS: C

4. ANS: D

5. ANS: A

6. ANS: B

7. ANS: C

8. ANS: A

9. ANS: A

10. ANS: D

11. ANS: A

12. ANS: D

13. ANS: A

14. ANS: B

15. ANS: A

16. ANS: C

17. ANS: A

18. ANS: C

19. ANS: B

20. ANS: C

21. ANS: B

22. ANS: D

23. ANS: A

24. ANS: B

25. ANS: A

26. ANS: B

27. ANS: D

28. ANS: A

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