Land Surveying

Trigonometry · Axiom Academy

LESSON Land Surveying: Triangulation Discover how surveyors use trigonometry to calculate irregular plot areas—essential for property boundaries, construction, and land development. Imagine you're a land surveyor tasked with measuring an irregularly-shaped property for sale. The plot has 5 sides with unequal lengths and angles. How do you calculate its area? The solution? Triangulation —breaking the irregular shape into triangles whose areas we can calculate using trigonometry! Click on the canvas to place boundary points of a property. The tool will automatically triangulate the plot and calculate the total area! Each triangle's area is calculated using two sides and the included angle —perfect for surveying where angles are measured with theodolites! • Side a (length 1) • Side b (length 2) • Angle C between them Area = ½ × a × b × sin(C) The sine function converts the angle into the height component! Universal Method: Works for any irregular polygon Practical Measurements: Only need side lengths and angles High Accuracy: Minimizes cumulative errors Easy Verification: Can check by summing triangle areas A triangular plot has sides of 40m and 50m with an included angle of 60°. What is its area? Calculate: A = ½ × 40 × 50 × sin(60°) (Hint: sin(60°) ≈ 0.866) Triangulation isn't just for land surveying—it's used across many fields where precise area measurements are critical. Calculate land areas for building permits, property valuations, and site planning.

This is the written version of the interactive lesson above. See the full Trigonometry course.