Mathematics Stage 5 Trigonometry and Google Maps

Mathematics Stage 5 – Trigonometry and Google Maps

Outcomes Assessed MA5.2-1WM selects appropriate notations and conventions to communicate mathematical ideas and solutions MA5.2-2WM interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems MA5.2-13MG applies trigonometry to solve problems, including problems involving bearings

Task Description  In groups, solve a problem requiring the application of trigonometry to a practical situation. This problem will be given to you by the teacher, and each group receives a different problem.  The problem solution will involve using Google Earth to obtain real measurements  The fully worked solution must be presented to the class using whatever ICT the group decides most clearly enhances explanation of the solution.  The group must make up a similar problem, modelled on their problem, and present it to the class for the class to solve.  All students must also complete peer assessment of other groups’ presentations, and self assessment of their own work.

Assessment  Teacher assessment: The group solution will be assessed by the teacher according to the criteria given below  Peer assessment: Each of the watching students will complete a survey rating each group’s presentation, and the ease with which they were able to solve the problem generated by each group.  Self Assessment: Each student reflects on the process and their learning in a short questionnaire Assessment Criteria

Criteria Mark Scale

Relevant information obtained from Google Earth 3-0

Diagram of right-angled triangle(s) that correctly represents the problem, and 3-0 includes sides and angles needed to solve the problem Full working explaining how Google Earth measurements of bearings, elevations, 4-0 building heights, distances etc. have been used to find the sides and angles needed to solve the problem. All angles given in degrees and minutes Unknown side/angle/area found with full working shown, and any angles used 3-0 given in degrees and minutes Problem answered with a full sentence 2-0

Clearly explains the solution to peers using appropriate language/diagrams/ICT 4-0 applications Writes an appropriate question that uses the skills explained in the example 3-0 problem Peer assessment mark for clarity of explanation 3-0

Peer assessment mark for ease of their solution 3-0

Peer assessment mark for correctness of their solutions 3-0

Self-assessment completed with full sentences indicating a genuine attempt at 4-0 reflection Problem One

You are going on holiday to Lord Howe Island. You are staying at a holiday house shown below. You need to find how far east and how for North the surf club is from the holiday house.

Instructions:

 Open the Google Earth file “Holiday House”. This will automatically open Google Earth to the holiday house shown above.

 Use the ruler tool to find the distance and bearing of the surf club from the holiday house.

 Use trigonometry to find how far east the surf club is from the holiday house. (The green line on the diagram)

 Use trigonometry to find how far north the surf club is from the holiday house. (The blue line on the diagram) Problem Two

You are going on holiday to Fraser Island. You are camping at the campsite shown below. You want to hike to the small lake shown below, and you need to find how far south and how far west the small lake is from the campsite.

Instructions:

 Open the Google Earth file “Campsite”. This will automatically open Google Earth to the campsite shown above.

 Use the ruler tool to find the distance and bearing of the small lake from the campsite.

 Use trigonometry to find how far west small lake is from the campsite.

 Use trigonometry to find how far south the small lake is from the campsite.

 Remember that you can print the Google earth file as a PDF and then edit the picture, including adding text and diagrams with Acrobat Pro extended. Problem Three

You are a builder costing the price for a new road in a housing development in Wollongong. The planned road is quite steep, and you need to determine if your Caterpillar 12G Motor Grader has enough power to build the road, or if you will have to hire a larger vehicle to cope with the slope. To avoid the expense of a surveyor, you are going to use Google maps to find the angle of elevation of the proposed road. The 12G Motor grader only performs well if the angle of elevation is less than 10o.

Instructions:

 Open the Google Earth file “end of road”. This will automatically open Google Earth to the end of the proposed road shown above.

 Use the ruler tool to find the distance of the proposed road.

 Move the mouse to the end of the road to find the elevation of the end of the road (it appears at the bottom of the screen)

 Move the mouse to the beginning of the road to find the elevation of the beginning of the road.

 Use trigonometry to find the angle of elevation from the beginning of the road to the end of the road.

 Determine if the 12G grader is suitable  Remember that you can print the Google earth file as a PDF and then edit the picture, including adding text and diagrams with Acrobat Pro.

Problem Four

You are planning to buy a house in Taroona, Hobart. It is built in front of a steep slope that may be unstable and subject to landslip. Based on a geotechnical engineer’s advice for this soil type, a slope of between 10o and 15o will double the risk of landslip, and home insurance costs will also double. A slope of more than 15o will increase the risk of landslip so much that home insurance will be impossible. To avoid the expense of a surveyor, you are going to use Google maps to find the angle of elevation of the slope, and so determine if you should buy the house.

Instructions:

 Open the Google Earth file “Top of Slope”. This will automatically open Google Earth to the top of the slope shown above.

 Use the ruler tool to find the distance of the slope to the back of the house.

 Move the mouse to the top of the slope to find its elevation of the end of the road (it appears at the bottom of the screen)

 Move the mouse to the back of the house to find its elevation.

 Use trigonometry to find the angle of elevation from the back of the house to the top of the slope.  Determine if insurance will be expensive, or impossible

 Remember that you can print the Google earth file as a PDF and then edit the picture, including adding text and diagrams with Acrobat Pro.

Problem Five

You are a marine biologist planning an investigation of the fish stocks in the Gulf of St Vincent. Before you begin your study, you need an estimate of the area of the Gulf. To avoid the expense of a surveyor, you are going to use Google maps to find the area of a triangle that approximates the Gulf of St Vincent.

Instructions:

 Open the Google Earth file “Gulf of St Vincent”. This will automatically open Google Earth to the top of the slope shown above.

 Pick two points close to the mouth of the gulf, as shown above.

 Use the ruler tool to find the bearing and distance of the eastern point from the place marker at the head of the gulf.  Use the ruler tool to find the bearing and distance of the western point from the place marker at the head of the gulf.

 Use the two bearings to find the angle at the top of the triangle

 Use trigonometry to find the area of the triangle. Remember the problem you solved involving the area of the triangular field.

Problem Six

You are a farmer who needs to need to find the area of an irregular shaped field, in order to calculate the costs of fertilizer for the field. To avoid the expense of a surveyor, you are going to use Google maps to get measurements that will help you calculate the field area.

Instructions:

 Open the Google Earth file “Centre of irregular field”. This will automatically open Google Earth to the centre of the field shown above.  Use the ruler tool to find the bearing and distance of each corner from the centre of the field, along the blue lines as shown above.

 The blue lines have divided the field into four triangles. Use the bearings to find the four angles at the centre of the field.

 Use trigonometry to find the area of each triangle. Remember the problem you solved involving the area of the triangular field.