Trigonometry Triangle Area Challenge

Name:

Date:

Triangle with angle and sides illustration

🔺 Triangle Area Challenge

Problem: A triangular piece of land has two sides measuring 15 metres and 20 metres, with an included angle of 60°. The local council needs to calculate the area of this land for development planning.

Part A: Draw and label the triangle with the given measurements.

Part B: Which trigonometric formula should you use to find the area? Circle the correct answer.

Area = ½ × base × height

Area = ½ × a × b × sin(C)

Area = a² + b² - 2ab cos(C)

Area = sin(A)/a = sin(B)/b

Part C: Show your working to calculate the area of the triangular land.

Part D: What is the final area? _____________ square metres

Part E: If the council charges $25 per square metre for development permits, what would be the total cost for this land?

🤔 Extension Challenge

Bonus Question: If you only knew that one side of the triangle was 15 metres, another side was 20 metres, and the angle opposite the 15-metre side was 30°, explain how you would find the area. What additional step would you need?