Law of Sines Trig Problem

Question

I'm experiencing a problem solving for an angle of a triangle using the law sines.

So I know the Angle $120$ degrees, the opposite of which is $13$. I know the opposite of the unknown angle which is $7$.

$$\frac{Sin(120)}{13}=\frac{Sin(A)}{7}$$ $$\frac{7*Sin(120)}{13}=Sin(A)$$ $$arcsin(\frac{7*Sin(120)}{13})=A$$ Why does this give me the wrong answer ~$64,62$?

Thanks in advance!

Answer 1

$\sin 120$ degrees $\approx 0.866$

$(0.866*7)/13 \approx 0.4663$

$\sin^{-1}(0.4663)\approx 27.795$

The mistake you are probably making is that you are not putting parenthesis correctly around your expression.

$\cfrac{\sin 120}{13*7}\ne \cfrac{\sin 120*7}{13}$

For example: $\sin^{-1} 12+1 \ne \sin^{-1} (12+1)$

Or, maybe it is doing $\sin \left(\cfrac{120}{13}\right)$ instead of $\cfrac{\sin (120)}{13}$.

Answer 2

Let check that the calculator is taking degrees and not radians for 120.

To check verify that you obtain $\sin (120) = \frac{\sqrt3}{2}$.