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