Help!!The figure shows the dimensions of a sail for a model boat. What is the area of this sail?Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth. Image Attached

First, we are going to use the law of cosines to find the unknown side of our triangle. Remember that the law of cosines formula is: [tex]c= \sqrt{a^{2}+b^{2}-2abCosC} [/tex]
For the image we can infer that [tex]a=7[/tex], [tex]b=8[/tex], and [tex]C=50[/tex]. So lets replace those values in our formula:
[tex]c= \sqrt{7^{2}+8^{2}-2(7)(8)Cos50} [/tex]
[tex]c=6.4[/tex]

Now that we have all of the sides of our triangle, we are going to use the semi-perimeter formula to find its semi-perimeter: 
[tex]s= \frac{a+b+c}{2} [/tex]
[tex]s= \frac{7+8+6.4}{2} [/tex]
[tex]s= \frac{21.4}{2} [/tex]
[tex]s=10.7[/tex]

Finally, now that we have the semi-perimeter of our triangle, we can use Heron's formula to find its area:
[tex]A= \sqrt{s(s-a)(s-b)(s-c)} [/tex]
[tex]A= \sqrt{10.7(10.7-7)(10.7-8)(10.7-6.4)} [/tex]
[tex]A= \sqrt{10.7(3.7)(2.8)(4.3)} [/tex]
[tex]A= \sqrt{476.6636} [/tex]
[tex]A=21.8[/tex]

We can conclude that the area of the sail of our boat is 21.8 [tex]cm^2[/tex].