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Stateline: Mapping farmland: using area and trigonometry

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A herd of cattle
Stateline: Mapping farmland: using area and trigonometry

SUBJECTS:  Maths

YEARS:  F7–8, 9–10


In northern Queensland's Gulf region, some farmers use GPS mapping to help manage their extensive properties.

Use this clip as a context for applying your understanding of area, in particular your understanding of conversion between square kilometres and hectares. Apply trigonometry and Pythagoras' theorem.


Things to think about

  1. 1.Imagine a rectangular farm property of 3000 square km, with a width of 20 km and length of 150 km. As 1 km2 = 100 ha, how many hectares would this be? Select from the following: 300 000 ha, 30 000 ha, 3 000 000 ha. Take a property three times as large. What could be the dimensions of a farm if it were 9000 km2 in size?
  2. 2.What reason does Simon Terry give for dividing his land into smaller areas? Take a close look at the map of Barry Hughes' North Head Station. The blue labels are dams on the property. How might this influence the way the areas of land are divided?
  3. 3.Imagine mapping a triangular area of land on a quad bike. Ride directly north 2000 m then turn 60 degrees clockwise from north and ride in a straight line for 1500 m. At this point, follow a ridge straight back to your starting point. Draw this journey. Use the ridge as the hypotenuse and extend the first north distance to form a right-angled triangle. Use trigonometry (cosine function) and then Pythagoras' theorem (a2 + b2 = c2) to calculate the distance you travelled along the ridge. (For your answer choose from 3341 m, 3041 m and 9250 m.)
  4. 4.Use ½ x base x height to calculate the area of your grazing land, which is the shape of an obtuse triangle. Hint: the height of this grazing land will be the distance you travelled east. Use sine function to work this out.



Date of broadcast: 6 Nov 2009


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