Trigonometry Test



Trigonometry & Finance

Practice Test

Name:_________________________________ Date:_________________

|Learning Goal |Beginning |Developing |Proficient |Sophisticated |

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

|I can calculate gross and net income | | | | |

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

|Developing Level |

|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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|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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|Proficient |

|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] |

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|Sophisticated |

|Find the area of the below triangle (A = ½ bh) |A ladder leaning against a house makes an angle of 30° with the ground. The |

|[pic] |foot of the ladder is 7 feet from the foot of the house. How long is the |

| |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

|Developing |

|Find the missing angle |Find the missing angle |

|[pic] |[pic] |

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|Find the missing angle |Find the missing angle |

|[pic] |[pic] |

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|Proficient |

|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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|Sophisticated |

|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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Learning Goal #3: I can calculate the gross and net income

|Developing Level |

|Complete the type of earnings in each scenario below. |Jacqueline works at Zia’s. She earns a base salary of $11.20/hr. On |

|Scenario |Saturday she worked 8 hours and billed her customers $1250.00. She earns an|

|Type of Income |average of 15% tips. What was Jacqueline's gross income for Saturday? |

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|Jack works at the Beanery and gets paid $12.65 per hour | |

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|Sam works for the District of Summerland and earns $45,000 per year | |

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|Susie works as a carpenter and gets on average $5000.00 per house | |

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|Tommy sells clothes at FreshAir and earns 5% of what he sells | |

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|Samantha was just hired as a legal assistant. Her salary is $65,500.00. |Sally works at a restaurant that is open for breakfast and sometimes lunch, |

|How much does she get paid each pay period if she gets her cheques: |but then open late in the evening for dinner. She often works a split |

| |shift. Calculate her hours worked for the week. |

|a. monthly: ______________________________ |Day |

|b. semimonthly: __________________________ |1st Shift |

|c. biweekly: _____________________________ |2nd Shift |

| |Total Hrs |

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| |Monday |

| |6am – 12pm |

| |5:15pm -8pm |

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| |Tuesday |

| |7am – 11:30am |

| |3:30pm – 6:15pm |

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| |Wednesday |

| |5:30am – 9:30am |

| |4pm – 9pm |

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| |Thursday |

| |6:30am – 10:15am |

| |5pm – 9pm |

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| |Friday |

| |6:30am – 9:15am |

| |4pm – 7:30pm |

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| |TOTAL |

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|Proficient |

|Lee works as an assistant to a florist. She can be paid $2.75 for every |Here is your pay stub: |

|arrangement or $13.25 per hour. Lee estimates that she could create about |[pic] |

|five arrangements an hour. What payment scheme would you recommend for Lee |What is this employee’s hourly rate? _____________ |

|and why? |How many hours were worked this pay period? ______ |

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|You make $17.50 an hour plus commission. You work 25 hours on week and make|Autumn has a weekly income of $395.97 and is assigned claim code 1. |

|a total of $837.50. What was the rate of commission on the $7890 of |Calculate her total weekly deductions and taxes. |

|merchandise you sold? |Deduction |

| |Amount |

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| |Federal Tax |

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| |Provincial Tax |

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| |CPP |

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| |EI |

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| |Total Deductions |

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|Sophisticated |

|You are comparing two options for summer jobs. One job is as a camp counsellor for 10 year olds and take place at your local community centre. The pay |

|is $240.00 a week for a period of 6 weeks. The other job is working as a house painter. It would require you to commute to different locations and pays|

|a rate of $11.50/hour. You can work 8.5 weeks at this job. |

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|What factors do you think you need to consider? |

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|Which job would you choose and why? |

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