Trigonometry Test



Trigonometry Practice Test

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|Learning Goal |Novice |Apprentice |Expert |

|I can find an unknown length of a triangle using trigonometry | | | |

|I can find an unknown angle of a triangle using trigonometry | | | |

Learning Goal #1: I can find an unknown length of a triangle using trigonometry

|Novice |

|Telephone poles are kept up with guy wires as shown. A worker says the |Label the sides of the triangle with hypotenuse, adjacent, and opposite |

|angles of inclination of the wires are the same. Is the student correct? |given θ is angle G |

|Justify your answer | |

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|Determine the length of side e to the nearest tenth of a centimetre. |Determine sin F nearest hundredth |

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|Label the sides of the triangle with their appropriate vocab name: |Find the height of side h. Show your work. |

|[pic] |[pic] |

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|Apprentice |

|Find the length of side x |Find the length of side x |

|[pic] |[pic] |

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|Find the length of side x |Find the length of side x |

|[pic] |[pic] |

|Find the length of side x |Find the length of side x |

|[pic] |[pic] |

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|Expert |

|Find the area of the below triangle (A = ½ bh) |Find the area of the below triangle (A = ½ bh) |

|[pic] |Z[pic] |

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|The angle of elevation of the sun is 15°. How long is the shadow of a 64 m |A ladder leaning against a house makes an angle of 30° with the ground. The |

|tall building? Justify your answer by showing work, including a labeled |foot of the ladder is 7 feet from the foot of the house. How long is the |

|diagram. |ladder? |

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|You are a block away from a skyscraper that is 780 feet tall. Your friend is|What is the distance across the suspension bridge? |

|between the skyscraper and yourself. The angle of elevation from your |[pic] |

|position to the top of the skyscraper is 42°. The angle of elevation from | |

|your friend’s position to the top of the skyscraper is 71°. To the nearest | |

|foot, how far are you from your friend? | |

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|[pic] | |

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Learning Goal #2: I can find an unknown angle of a triangle using trigonometry

|Novice |

|Find the missing angle |Find the missing angle |

|[pic] |[pic] |

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|Find the missing angle |Find the missing angle |

|[pic] |[pic] |

|Apprentice |

|What is the angle of elevation if you are standing 400 ft away from the base of a |A ladder leans against a brick wall. The foot of the ladder is 6 feet|

|850 ft tall building? |from the wall. The ladder reaches a height of 15 feet on the wall. |

|[pic] |Find to the nearest degree, the angle the ladder makes with the wall.|

| |[pic] |

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|What angle is the airplane landing from? |An 8 foot metal guy wire is attached to a broken stop sign to secure |

|[pic] |its position until repairs can be made. Attached to a stake in the |

| |ground, the guy wire makes an angle of 51º with the ground. How far |

| |from the foot of the stop sign is the stake, to the nearest tenth of |

| |a metre?  |

| |[pic] |

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|Expert |

|The Uniform Federal Accessibility Standards specify that the ramp angle used|It is important to consider the tapering of the strings and neck when |

|for a wheelchair ramp must be less than or equal to 4.78°. You want to build|building a guitar. The tapering affects the tone that the strings make. For |

|a ramp with a vertical rise of 0.5 m. You want to minimize the horizontal |the guitar shown, suppose the width of the neck is tapered from 56 mm to 44 |

|distance taken up by the ramp but still meet the Uniform Federal |mm over a length of 650 mm. What is the angle of the taper for one side of |

|Accessibility Standards. Draw a sketch showing the approximate dimensions of|the guitar strings? |

|your ramp. Justify your solution by showing your equations. |[pic] |

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