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Mathematics Stage 5 - Using trigonometry to find the area of a scalene triangle Outcomes Assessed MA5.1-1WM - uses appropriate terminology, diagrams and symbols in mathematical contexts MA5.1-2WM - selects and uses appropriate strategies to solve problems MA5.1-8MG - calculates the areas of composite shapes, and the surface areas of rectangular and triangular prisms MA5.1-10MG - applies trigonometry, given diagrams, to solve problems, including problems involving angles of elevation and depression Task A farmer wants to find the area of a triangular field. Unfortunately the surveyor was only able to provide the information shown below. What is the exact area of the field? 550m 30o 700m Hint 1: Draw a bounding rectangle around the triangle as shown below. Remember that the area of a triangle is half the area of the bounding rectangle. 550m 30o 700m Hint 2: Use trigonometry to find the width of the triangle Hint 3: The width of the rectangle can be found using the dotted triangle shown below. 550m 30o 700m