Model and solve problems that involve the sine rule, cosine rule and the area formula in two - and three-dimensional contexts (including bearings, directions and angles of elevation and depression), with and without technology. Mathematical Methods 2025 v1.3

A surveyor measures a triangular plot of land and determines that two sides are $48 \text{ m}$ and $65 \text{ m}$, with the included angle of $52°$. Which of the following is the area of the plot, to the nearest square metre?

A surveyor measures a triangular parcel of land. Two adjacent sides of the triangle measure 85 m and 120 m, and the included angle between them is $42°$. (a) Determine the area of the land parcel, to the nearest square metre. [1 mark] (b) Calculate the third side of the triangle, correct to 1 decimal place. [2 marks]