Answer:
Cost= 69,713 $
Step-by-step explanation:
as we have two sides and an angle we apply the law of cosine
[tex]a^{2}=b^{2}+c^{2}-2bc*cosA\\a^{2}=140^{2}+200^{2}-2*140*200*cos60\\a^{2}=19600+40000-56000*0.5\\a^{2}=31600;a=\sqrt{31600}=177.76[/tex],
we must find h, so
[tex]sin60=\frac{H}{b}[/tex]
[tex]H=b*sin60=140*\frac{\sqrt{3}}{2}=121.24[/tex]
finally
[tex]A_{lt}=\frac{b*h}{2}=\frac{200*121.24}{2}=12,124ft^{2}[/tex]
the cost of the triangle piece of land is:
Cost=5.75 $/ft2 * 12.124ft2 = 69,713 $
