step 1
Find the measure of the third angle
REmember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
In this problem
x+65+55=180
solve for x
x+120=180
x=60 degrees
step 2
Find the area of triangle
Applying the law of sines
[tex]A=\frac{1}{2}\cdot a\cdot b\cdot\sin (x)[/tex]
we have
a=120 m
b=132.8 m
X=60 degrees
substitute
[tex]\begin{gathered} A=\frac{1}{2}\cdot120\cdot132.8\cdot\sin (60^o) \\ A=6,900.5\text{ m\textasciicircum{}2} \end{gathered}[/tex]
area is 6,900.5 square meters
