sin law

Sorry, Mathcad, but.....

sin(70) ≠ sin(40)cos(30) +cos(30)sin(40)

sin(70) = sin(40)cos(30) + sin(30)cos(40)

And .... 8sin(40)/sin (70) = Melody's answer  ...... which is not =   8/√3  = 4.6188021535170061

$${\frac{{\mathtt{8}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{40}}^\circ\right)}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{70}}^\circ\right)}}} = {\mathtt{5.472\: \!322\: \!293\: \!214\: \!088\: \!1}}$$

11.7 Yo Welcome

.Melody,I don't think simply plugging in values is what the question is really about.This is testing one's knowledge of the addition formulae,properties of triangles and manipulation of fractions.  As below:

sin(a+b)=sin(a)cos(b) +cos(a)sin(b) so you can write sin70 as 

sin(70)=sin(40)cos(30) +cos(30)sin(40)

Now the expression reads

8sin(40)/sin(40)cos(30)+cos(30)sin(40).One should also know (from the equilateral triangle) that cos(30)=1/sqrt2.

So now all we have to do is simplify a fraction,getting

8sin(40)/sin(70)= 8sin(40)/(1/sqrt2sin(40) +1/sqrt2sin(40)

                         =8sin(40)/(2/sqrt2sin(40)

                          =8sin(40)/sqrt2sin(40)

Now the sin(40)'s cancel and all you have to do is resolve 8/sqrt2 and the answer is 4 times root 2.

slight correction,cos(30) is (sqrt3)/2.Amend accordingly,and solution drops out as 

8/(sqrt3). Which still gives you Melody's answer of course.

Come on Melody, you have to respond to that (mostly) garbage.

Come on anon, mathcad has answered in good faith.

We all learn from our errors :)

I am glad that you got involved mathcad :)