So we know the Law of Sines which is that Sin A/a = Sin B/b = Sin C/c. The Sin on top of the fraction is the angle, and the letter on the bottom is the side opposite from that angle.

Our first step is going to be finding the last angle. We have 2 angles already, but one that's missing. We know that all triangles' angles add up to 180, so we can add 68+40=108. Then do 180-108 to get 72. Now we know the third and final angle.

Ok so back to Law of Sines. Now we can plug into that equation. We only need Sin A/a = Sin B/b (It doesn't matter what order you put them in). And remember the lowercase letter at the bottom represents the OPPOSITE side from one of the angles. Since the problem wants the side opposite Sin 68, let's set up a proportion.

$\frac{Sin72}{7} =\frac{Sin 68}{x}$

Set up we have what we know. We know one side, and opposite that is the angle we already solved for. Now we can cross multiply and end up with:

$x (Sin 72)= 7(Sin 68)$

Since we want to isolate x, we can divide each side by Sin 72.

x= 7(Sin 68)/Sin 72

So now let's put it into the calculator:

7(Sin 68)=6.2853

Now let's divide 6.2853/Sin 72

And you should be left with 6.82 if you round it!

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3 years ago