Hello!
The answer is:
The area of the triangle is:
[tex]Area=13.2cm^{2}[/tex]
Why?
We can solve the problem using the Side-Angle-Side (SAS) method, to calculate the area of a triangle given two sides and a single angle.
The SAS method to calculate the area of a triangle is given by the following the equation:
[tex]Area=\frac{abSinC}{2}[/tex]
Where,
a and b are the known sides.
C is the known angle
Now, we are given a triangle with the following dimension:
[tex]Side_{a}=7cm\\Side_{b}=8cm\\\alpha=28\°[/tex]
Then, using the information and solving we have:
[tex]Area=\frac{7cm*8cm*Sin(28\°)}{2}[/tex]
[tex]Area=\frac{56cm^{2}*Sin(28\°)}{2}\\\\Area=\frac{56cm^{2}*0.47}{2}\\\\Area=\frac{26.32cm^{2}}{2}\\\\Area=13.16cm^{2}[/tex]
Hence, the area of the triangle, rounded to the nearest tenth is:
[tex]Area=13.2cm^{2}[/tex]
Have a nice day!
