Given that SRT is a triangle with base RT as 150 m, and side RS as 75 m, and the included angle R as 40 degrees.
Construction: Draw a perpendicular from S onto base RT at point M. Then SM will represent the height of the triangle.
The corresponding diagram is given below,
Apply the sine ratio in the triangle SMR,
[tex]\begin{gathered} \sin \theta=\frac{\text{ Opposite Side}}{\text{ Hypotenuse}} \\ \sin 40^{\circ}=\frac{SM}{RS} \\ 0.643=\frac{SM}{75} \\ SM=0.643\times75 \\ SM=48.225 \end{gathered}[/tex]
Now, solve for the area of the triangle as,
[tex]\begin{gathered} Area=\frac{1}{2}\times base\times height \\ Area=\frac{1}{2}\times RT\times SM \\ Area=\frac{1}{2}\times150\times48.225 \\ Area=3616.875 \\ Area\approx3616.9 \end{gathered}[/tex]
Thus, the area of the given triangle is 3616.9 square meters approximately.
