Question

A local park is located on a triangular piece of land.What is the area of the park to the nearest tenth?

Answer 1

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,

`\begin{gathered} \sin \theta=\frac{\text{ Opposite Side}}{\text{ Hypotenuse}} \\ \sin 40^(\circ)=(SM)/(RS) \\ 0.643=(SM)/(75) \\ SM=0.643*75 \\ SM=48.225 \end{gathered}`

Now, solve for the area of the triangle as,

`\begin{gathered} Area=(1)/(2)* base* height \\ Area=(1)/(2)* RT* SM \\ Area=(1)/(2)*150*48.225 \\ Area=3616.875 \\ Area\approx3616.9 \end{gathered}`

Thus, the area of the given triangle is 3616.9 square meters approximately.